Strong and weak primes

From Rosetta Code
Task
Strong and weak primes
You are encouraged to solve this task according to the task description, using any language you may know.


Definitions   (as per number theory)
  •   The   prime(p)   is the   pth   prime.
  •   prime(1)   is   2
  •   prime(4)   is   7
  •   A   strong   prime   is when     prime(p)   is   >   [prime(p-1) + prime(p+1)] ÷ 2
  •   A     weak    prime   is when     prime(p)   is   <   [prime(p-1) + prime(p+1)] ÷ 2


Note that the definition for   strong primes   is different when used in the context of   cryptography.


Task
  •   Find and display (on one line) the first   36   strong primes.
  •   Find and display the   count   of the strong primes below   1,000,000.
  •   Find and display the   count   of the strong primes below 10,000,000.
  •   Find and display (on one line) the first   37   weak primes.
  •   Find and display the   count   of the weak primes below   1,000,000.
  •   Find and display the   count   of the weak primes below 10,000,000.
  •   (Optional)   display the   counts   and   "below numbers"   with commas.

Show all output here.


Related Task


Also see



11l[edit]

F primes_upto(limit)
   V is_prime = [0B] * 2 [+] [1B] * (limit - 1)
   L(n) 0 .< Int(limit ^ 0.5 + 1.5)
      I is_prime[n]
         L(i) (n * n .< limit + 1).step(n)
            is_prime[i] = 0B
   R enumerate(is_prime).filter((i, prime) -> prime).map((i, prime) -> i)

V p = primes_upto(10'000'000)
[Int] s, w, b
L(i) 1 .< p.len - 1
   I p[i] > (p[i - 1] + p[i + 1]) * 0.5
      s [+]= p[i]
   E I p[i] < (p[i - 1] + p[i + 1]) * 0.5
      w [+]= p[i]
   E
      b [+]= p[i]

print(‘The first   36   strong primes: ’s[0.<36])
print(‘The   count   of the strong primes below   1,000,000: ’sum(s.filter(p -> p < 1'000'000).map(p -> 1)))
print(‘The   count   of the strong primes below  10,000,000: ’s.len)
print("\nThe first   37   weak primes: "w[0.<37])
print(‘The   count   of the weak   primes below   1,000,000: ’sum(w.filter(p -> p < 1'000'000).map(p -> 1)))
print(‘The   count   of the weak   primes below  10,000,000: ’w.len)
print("\n\nThe first   10 balanced primes: "b[0.<10])
print(‘The   count   of balanced   primes below   1,000,000: ’sum(b.filter(p -> p < 1'000'000).map(p -> 1)))
print(‘The   count   of balanced   primes below  10,000,000: ’b.len)
print("\nTOTAL primes below   1,000,000: "sum(p.filter(pr -> pr < 1'000'000).map(pr -> 1)))
print(‘TOTAL primes below  10,000,000: ’p.len)
Output:
The first   36   strong primes: [11, 17, 29, 37, 41, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 163, 179, 191, 197, 223, 227, 239, 251, 269, 277, 281, 307, 311, 331, 347, 367, 379, 397, 419, 431, 439]
The   count   of the strong primes below   1,000,000: 37723
The   count   of the strong primes below  10,000,000: 320991

The first   37   weak primes: [3, 7, 13, 19, 23, 31, 43, 47, 61, 73, 83, 89, 103, 109, 113, 131, 139, 151, 167, 181, 193, 199, 229, 233, 241, 271, 283, 293, 313, 317, 337, 349, 353, 359, 383, 389, 401]
The   count   of the weak   primes below   1,000,000: 37780
The   count   of the weak   primes below  10,000,000: 321749


The first   10 balanced primes: [5, 53, 157, 173, 211, 257, 263, 373, 563, 593]
The   count   of balanced   primes below   1,000,000: 2994
The   count   of balanced   primes below  10,000,000: 21837

TOTAL primes below   1,000,000: 78498
TOTAL primes below  10,000,000: 664579

ALGOL 68[edit]

Works with: ALGOL 68G version Any - tested with release 2.8.3.win32
# find and count strong and weak primes                                       #
PR heap=128M PR # set heap memory size for Algol 68G                          #
# returns a string representation of n with commas                            #
PROC commatise = ( INT n )STRING:
     BEGIN
        STRING result      := "";
        STRING unformatted  = whole( n, 0 );
        INT    ch count    := 0;
        FOR c FROM UPB unformatted BY -1 TO LWB unformatted DO
            IF   ch count <= 2 THEN ch count +:= 1
            ELSE                    ch count  := 1; "," +=: result
            FI;
            unformatted[ c ] +=: result
        OD;
        result
     END # commatise # ;
# sieve values                                                                #
CHAR prime     = "P"; #  unclassified/average prime                           #
CHAR strong    = "S"; #                strong prime                           #
CHAR weak      = "W"; #                  weak prime                           #
CHAR composite = "C"; #                   non-prime                           #
# sieve of Eratosthenes: sets s[i] to prime if i is a prime,                  #
#                                     composite otherwise                     #
PROC sieve = ( REF[]CHAR s )VOID:
     BEGIN
        # start with everything flagged as prime                              #
        FOR i TO UPB s DO s[ i ] := prime OD;
        # sieve out the non-primes                                            #
        s[ 1 ] := composite;
        FOR i FROM 2 TO ENTIER sqrt( UPB s ) DO
            IF s[ i ] = prime THEN FOR p FROM i * i BY i TO UPB s DO s[ p ] := composite OD FI
        OD
     END # sieve # ;

INT max number = 10 000 000;
# construct a sieve of primes up to slightly more than the maximum number     #
# required for the task, as we may need an extra prime for the classification #
[ 1 : max number + 1 000 ]CHAR primes;
sieve( primes );
# classify the primes                                                         #
# find the first three primes                                                 #
INT prev prime := 0;
INT curr prime := 0;
INT next prime := 0;
FOR p FROM 2 WHILE prev prime = 0 DO
    IF primes[ p ] = prime THEN
        prev prime := curr prime;
        curr prime := next prime;
        next prime := p
    FI
OD;
# 2 is the only even prime so the first three primes are the only case where  #
# the average of prev prime and next prime is not an integer                  #
IF   REAL avg = ( prev prime + next prime ) / 2;
     curr prime > avg THEN primes[ curr prime ] := strong
ELIF curr prime < avg THEN primes[ curr prime ] := weak  
FI;
# classify the rest of the primes                                             #
FOR p FROM next prime + 1 WHILE curr prime <= max number DO
    IF primes[ p ] = prime THEN
        prev prime := curr prime;
        curr prime := next prime;
        next prime := p;
        IF   INT avg = ( prev prime + next prime ) OVER 2;
             curr prime > avg THEN primes[ curr prime ] := strong
        ELIF curr prime < avg THEN primes[ curr prime ] := weak  
        FI
    FI
OD;
INT strong1 := 0, strong10 := 0;
INT weak1   := 0, weak10   := 0;
FOR p WHILE p < 10 000 000 DO
    IF   primes[ p ] = strong THEN
        strong10 +:= 1;
        IF p < 1 000 000 THEN strong1 +:= 1 FI
    ELIF primes[ p ] = weak   THEN
        weak10   +:= 1;
        IF p < 1 000 000 THEN weak1   +:= 1 FI
    FI
OD;
INT strong count  := 0;
print( ( "first 36 strong primes:", newline ) );
FOR p WHILE strong count < 36 DO IF primes[ p ] = strong THEN print( ( " ", whole( p, 0 ) ) ); strong count +:= 1 FI OD;
print( ( newline ) );
print( ( "strong primes below   1,000,000: ", commatise(  strong1 ), newline ) );
print( ( "strong primes below  10,000,000: ", commatise( strong10 ), newline ) );
print( ( "first 37   weak primes:", newline ) );
INT weak count    := 0;
FOR p WHILE weak count   < 37 DO IF primes[ p ] = weak   THEN print( ( " ", whole( p, 0 ) ) );   weak count +:= 1 FI OD;
print( ( newline ) );
print( ( "  weak primes below   1,000,000: ", commatise(    weak1 ), newline ) );
print( ( "  weak primes below  10,000,000: ", commatise(   weak10 ), newline ) )
Output:
first 36 strong primes:
 11 17 29 37 41 59 67 71 79 97 101 107 127 137 149 163 179 191 197 223 227 239 251 269 277 281 307 311 331 347 367 379 397 419 431 439
strong primes below   1,000,000: 37,723
strong primes below  10,000,000: 320,991
first 37   weak primes:
 3 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181 193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401
  weak primes below   1,000,000: 37,780
  weak primes below  10,000,000: 321,750

AWK[edit]

# syntax: GAWK -f STRONG_AND_WEAK_PRIMES.AWK
BEGIN {
    for (i=1; i<1E7; i++) {
      if (is_prime(i)) {
        arr[++n] = i
      }
    }
# strong:
    stop1 = 36 ; stop2 = 1E6 ; stop3 = 1E7
    count1 = count2 = count3 = 0
    printf("The first %d strong primes:",stop1)
    for (i=2; count1<stop1; i++) {
      if (arr[i] > (arr[i-1] + arr[i+1]) / 2) {
        count1++
        printf(" %d",arr[i])
      }
    }
    printf("\n")
    for (i=2; i<stop3; i++) {
      if (arr[i] > (arr[i-1] + arr[i+1]) / 2) {
        count3++
        if (arr[i] < stop2) {
          count2++
        }
      }
    }
    printf("Number below %d: %d\n",stop2,count2)
    printf("Number below %d: %d\n",stop3,count3)
# weak:
    stop1 = 37 ; stop2 = 1E6 ; stop3 = 1E7
    count1 = count2 = count3 = 0
    printf("The first %d weak primes:",stop1)
    for (i=2; count1<stop1; i++) {
      if (arr[i] < (arr[i-1] + arr[i+1]) / 2) {
        count1++
        printf(" %d",arr[i])
      }
    }
    printf("\n")
    for (i=2; i<stop3; i++) {
      if (arr[i] < (arr[i-1] + arr[i+1]) / 2) {
        count3++
        if (arr[i] < stop2) {
          count2++
        }
      }
    }
    printf("Number below %d: %d\n",stop2,count2)
    printf("Number below %d: %d\n",stop3,count3)
    exit(0)
}
function is_prime(n,  d) {
    d = 5
    if (n < 2) { return(0) }
    if (n % 2 == 0) { return(n == 2) }
    if (n % 3 == 0) { return(n == 3) }
    while (d*d <= n) {
      if (n % d == 0) { return(0) }
      d += 2
      if (n % d == 0) { return(0) }
      d += 4
    }
    return(1)
}
Output:
The first 36 strong primes: 11 17 29 37 41 59 67 71 79 97 101 107 127 137 149 163 179 191 197 223 227 239 251 269 277 281 307 311 331 347 367 379 397 419 431 439
Number below 1000000: 37723
Number below 10000000: 320992
The first 37 weak primes: 3 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181 193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401
Number below 1000000: 37781
Number below 10000000: 321750

C[edit]

Translation of: D
#include <stdbool.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>

const int PRIMES[] = {
    2, 3, 5, 7,
    11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,
    101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293,
    307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523,
    541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769,
    773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997,
    1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217,
    1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451,
    1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663,
    1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907,
    1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141,
    2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383,
    2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659,
    2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861,
    2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163
};
#define PRIME_LENGTH (sizeof(PRIMES) / sizeof(int))

bool isPrime(int n) {
    int i;

    if (n < 2) {
        return false;
    }

    for (i = 0; i < PRIME_LENGTH; ++i) {
        if (n == PRIMES[i]) {
            return true;
        }
        if (n % PRIMES[i] == 0) {
            return false;
        }
        if (n < PRIMES[i] * PRIMES[i]) {
            break;
        }
    }

    return true;
}

int main() {
    const int MAX_LENGTH = 700000;
    int i, n, c1, c2;

    int *primePtr = calloc(MAX_LENGTH, sizeof(int));
    if (primePtr == 0) {
        return EXIT_FAILURE;
    }

    for (i = 0; i < PRIME_LENGTH; i++) {
        primePtr[i] = PRIMES[i];
    }

    i--;
    for (n = PRIMES[i] + 4; n < 10000100;) {
        if (isPrime(n)) {
            primePtr[i++] = n;
        }
        n += 2;

        if (isPrime(n)) {
            primePtr[i++] = n;
        }
        n += 4;

        if (i >= MAX_LENGTH) {
            printf("Allocate more memory.");
            return EXIT_FAILURE;
        }
    }

    /////////////////////////////////////////////////////////////
    printf("First 36 strong primes:");
    c1 = 0;
    c2 = 0;
    for (n = 0, i = 1; i < MAX_LENGTH - 1; i++) {
        if (2 * primePtr[i] > primePtr[i - 1] + primePtr[i + 1]) {
            if (n < 36) {
                printf("  %d", primePtr[i]);
                n++;
            }
            if (primePtr[i] < 1000000) {
                c1++;
                c2++;
            } else if (primePtr[i] < 10000000) {
                c2++;
            } else break;
        }
    }
    printf("\nThere are %d strong primes below 1,000,000", c1);
    printf("\nThere are %d strong primes below 10,000,000\n\n", c2);

    /////////////////////////////////////////////////////////////
    printf("First 37 weak primes:");
    c1 = 0;
    c2 = 0;
    for (n = 0, i = 1; i < MAX_LENGTH - 1; i++) {
        if (2 * primePtr[i] < primePtr[i - 1] + primePtr[i + 1]) {
            if (n < 37) {
                printf("  %d", primePtr[i]);
                n++;
            }
            if (primePtr[i] < 1000000) {
                c1++;
                c2++;
            } else if (primePtr[i] < 10000000) {
                c2++;
            } else break;
        }
    }
    printf("\nThere are %d weak primes below 1,000,000", c1);
    printf("\nThere are %d weak primes below 10,000,000\n\n", c2);

    free(primePtr);
    return EXIT_SUCCESS;
}
Output:
First 36 strong primes:  11  17  29  37  41  59  67  71  79  97  101  107  127  137  149  163  179  191  197  223  227  239  251  269  277  281  307  311  331  347  367  379  397  419  431  439
There are 37722 strong primes below 1,000,000
There are 320990 strong primes below 10,000,000

First 37 weak primes:  3  7  13  19  23  31  43  47  61  73  83  89  103  109  113  131  139  151  167  181  193  199  229  233  241  271  283  293  313  317  337  349  353  359  383  389  401
There are 37780 weak primes below 1,000,000
There are 321750 weak primes below 10,000,000

C#[edit]

Works with: C sharp version 7
using static System.Console;
using static System.Linq.Enumerable;
using System;

public static class StrongAndWeakPrimes
{
    public static void Main() {
        var primes = PrimeGenerator(10_000_100).ToList();
        var strongPrimes = from i in Range(1, primes.Count - 2) where primes[i] > (primes[i-1] + primes[i+1]) / 2 select primes[i];
        var weakPrimes = from i in Range(1, primes.Count - 2) where primes[i] < (primes[i-1] + primes[i+1]) / 2.0 select primes[i];
        WriteLine($"First 36 strong primes: {string.Join(", ", strongPrimes.Take(36))}");
        WriteLine($"There are {strongPrimes.TakeWhile(p => p < 1_000_000).Count():N0} strong primes below {1_000_000:N0}");
        WriteLine($"There are {strongPrimes.TakeWhile(p => p < 10_000_000).Count():N0} strong primes below {10_000_000:N0}");
        WriteLine($"First 37 weak primes: {string.Join(", ", weakPrimes.Take(37))}");
        WriteLine($"There are {weakPrimes.TakeWhile(p => p < 1_000_000).Count():N0} weak primes below {1_000_000:N0}");
        WriteLine($"There are {weakPrimes.TakeWhile(p => p < 10_000_000).Count():N0} weak primes below {1_000_000:N0}");
    }
   
}
Output:
First 36 strong primes: 11, 17, 29, 37, 41, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 163, 179, 191, 197, 223, 227, 239, 251, 269, 277, 281, 307, 311, 331, 347, 367, 379, 397, 419, 431, 439
There are 37,723 strong primes below 1,000,000
There are 320,991 strong primes below 10,000,000
First 37 weak primes: 3, 7, 13, 19, 23, 31, 43, 47, 61, 73, 83, 89, 103, 109, 113, 131, 139, 151, 167, 181, 193, 199, 229, 233, 241, 271, 283, 293, 313, 317, 337, 349, 353, 359, 383, 389, 401
There are 37,780 weak primes below 1,000,000
There are 321,750 weak primes below 1,000,000

C++[edit]

#include <algorithm>
#include <iostream>
#include <iterator>
#include <locale>
#include <vector>
#include "prime_sieve.hpp"

const int limit1 = 1000000;
const int limit2 = 10000000;

class prime_info {
public:
    explicit prime_info(int max) : max_print(max) {}
    void add_prime(int prime);
    void print(std::ostream& os, const char* name) const;
private:
    int max_print;
    int count1 = 0;
    int count2 = 0;
    std::vector<int> primes;
};

void prime_info::add_prime(int prime) {
    ++count2;
    if (prime < limit1)
        ++count1;
    if (count2 <= max_print)
        primes.push_back(prime);
}

void prime_info::print(std::ostream& os, const char* name) const {
    os << "First " << max_print << " " << name << " primes: ";
    std::copy(primes.begin(), primes.end(), std::ostream_iterator<int>(os, " "));
    os << '\n';
    os << "Number of " << name << " primes below " << limit1 << ": " << count1 << '\n';
    os << "Number of " << name << " primes below " << limit2 << ": " << count2 << '\n';
}

int main() {
    prime_sieve sieve(limit2 + 100);

    // write numbers with groups of digits separated according to the system default locale
    std::cout.imbue(std::locale(""));

    // count and print strong/weak prime numbers
    prime_info strong_primes(36);
    prime_info weak_primes(37);
    int p1 = 2, p2 = 3;
    for (int p3 = 5; p2 < limit2; ++p3) {
        if (!sieve.is_prime(p3))
            continue;
        int diff = p1 + p3 - 2 * p2;
        if (diff < 0)
            strong_primes.add_prime(p2);
        else if (diff > 0)
            weak_primes.add_prime(p2);
        p1 = p2;
        p2 = p3;
    }
    strong_primes.print(std::cout, "strong");
    weak_primes.print(std::cout, "weak");
    return 0;
}

Contents of prime_sieve.hpp:

#ifndef PRIME_SIEVE_HPP
#define PRIME_SIEVE_HPP

#include <algorithm>
#include <vector>

/**
 * A simple implementation of the Sieve of Eratosthenes.
 * See https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes.
 */
class prime_sieve {
public:
    explicit prime_sieve(size_t);
    bool is_prime(size_t) const;
private:
    std::vector<bool> is_prime_;
};

/**
 * Constructs a sieve with the given limit.
 *
 * @param limit the maximum integer that can be tested for primality
 */
inline prime_sieve::prime_sieve(size_t limit) {
    limit = std::max(size_t(3), limit);
    is_prime_.resize(limit/2, true);
    for (size_t p = 3; p * p <= limit; p += 2) {
        if (is_prime_[p/2 - 1]) {
            size_t inc = 2 * p;
            for (size_t q = p * p; q <= limit; q += inc)
                is_prime_[q/2 - 1] = false;
        }
    }
}

/**
 * Returns true if the given integer is a prime number. The integer
 * must be less than or equal to the limit passed to the constructor.
 *
 * @param n an integer less than or equal to the limit passed to the
 * constructor
 * @return true if the integer is prime
 */
inline bool prime_sieve::is_prime(size_t n) const {
    if (n == 2)
        return true;
    if (n < 2 || n % 2 == 0)
        return false;
    return is_prime_.at(n/2 - 1);
}

#endif
Output:
First 36 strong primes: 11 17 29 37 41 59 67 71 79 97 101 107 127 137 149 163 179 191 197 223 227 239 251 269 277 281 307 311 331 347 367 379 397 419 431 439 
Number of strong primes below 1,000,000: 37,723
Number of strong primes below 10,000,000: 320,991
First 37 weak primes: 3 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181 193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401 
Number of weak primes below 1,000,000: 37,780
Number of weak primes below 10,000,000: 321,750

D[edit]

import std.algorithm;
import std.array;
import std.range;
import std.stdio;

immutable PRIMES = [
    2, 3, 5, 7,
    11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,
    101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293,
    307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523,
    541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769,
    773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997,
    1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217,
    1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451,
    1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663,
    1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907,
    1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141,
    2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383,
    2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659,
    2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861,
    2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163,
    3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391,
    3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637,
    3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907,
    3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153,
    4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423,
    4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679,
    4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967,
    4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231,
    5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501,
    5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749,
    5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043,
    6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299,
    6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571,
    6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841,
    6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121,
    7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451,
    7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681,
    7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951,
    7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263,
    8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563,
    8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819,
    8821, 8831, 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103,
    9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377,
    9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643,
    9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907,
    9923, 9929, 9931, 9941, 9949, 9967, 9973,
];

bool isPrime(int n) {
    if (n < 2) {
        return false;
    }

    foreach (prime; PRIMES) {
        if (n == prime) {
            return true;
        }
        if (n % prime == 0) {
            return false;
        }
        if (n < prime * prime) {
            if (n > PRIMES[$-1] * PRIMES[$-1]) {
                assert(false, "Out of pre-computed primes.");
            }
            break;
        }
    }

    return true;
}

void main() {
    auto primeList = iota(2, 10_000_100).filter!isPrime.array;

    int[] strongPrimes, weakPrimes;
    foreach (i,p; primeList) {
        if (i > 0 && i < primeList.length - 1) {
            if (p > 0.5 * (primeList[i - 1] + primeList[i + 1])) {
                strongPrimes ~= p;
            } else if (p < 0.5 * (primeList[i - 1] + primeList[i + 1])) {
                weakPrimes ~= p;
            }
        }
    }

    writeln("First 36 strong primes: ", strongPrimes[0..36]);
    writefln("There are %d strong primes below 1,000,000", strongPrimes.filter!"a<1_000_000".count);
    writefln("There are %d strong primes below 10,000,000", strongPrimes.filter!"a<10_000_000".count);

    writeln("First 37 weak primes: ", weakPrimes[0..37]);
    writefln("There are %d weak primes below 1,000,000", weakPrimes.filter!"a<1_000_000".count);
    writefln("There are %d weak primes below 10,000,000", weakPrimes.filter!"a<10_000_000".count);
}
Output:
First 36 strong primes: [11, 17, 29, 37, 41, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 163, 179, 191, 197, 223, 227, 239, 251, 269, 277, 281, 307, 311, 331, 347, 367, 379, 397, 419, 431, 439]
There are 37723 strong primes below 1,000,000
There are 320991 strong primes below 10,000,000
First 37 weak primes: [3, 7, 13, 19, 23, 31, 43, 47, 61, 73, 83, 89, 103, 109, 113, 131, 139, 151, 167, 181, 193, 199, 229, 233, 241, 271, 283, 293, 313, 317, 337, 349, 353, 359, 383, 389, 401]
There are 37780 weak primes below 1,000,000
There are 321750 weak primes below 10,000,000

Factor[edit]

USING: formatting grouping kernel math math.primes sequences
tools.memory.private ;
IN: rosetta-code.strong-primes

: fn ( p-1 p p+1 -- p sum ) rot + 2 / ;
: strong? ( p-1 p p+1 -- ? ) fn > ;
: weak? ( p-1 p p+1 -- ? ) fn < ;

: swprimes ( seq quot -- seq )
    [ 3 <clumps> ] dip [ first3 ] prepose filter [ second ] map
    ; inline

: stats ( seq n -- firstn count1 count2 )
    [ head ] [ drop [ 1e6 < ] filter length ] [ drop length ]
    2tri [ commas ] bi@ ;

10,000,019 primes-upto [ strong? ] over [ weak? ]
[ swprimes ] 2bi@ [ 36 ] [ 37 ] bi* [ stats ] 2bi@

"First 36 strong primes:\n%[%d, %]
%s strong primes below 1,000,000
%s strong primes below 10,000,000\n
First 37 weak primes:\n%[%d, %]
%s weak primes below 1,000,000
%s weak primes below 10,000,000\n" printf
Output:
First 36 strong primes:
{ 11, 17, 29, 37, 41, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 163, 179, 191, 197, 223, 227, 239, 251, 269, 277, 281, 307, 311, 331, 347, 367, 379, 397, 419, 431, 439 }
37,723 strong primes below 1,000,000
320,991 strong primes below 10,000,000

First 37 weak primes:
{ 3, 7, 13, 19, 23, 31, 43, 47, 61, 73, 83, 89, 103, 109, 113, 131, 139, 151, 167, 181, 193, 199, 229, 233, 241, 271, 283, 293, 313, 317, 337, 349, 353, 359, 383, 389, 401 }
37,780 weak primes below 1,000,000
321,750 weak primes below 10,000,000

FreeBASIC[edit]

#include "isprime.bas"

function nextprime( n as uinteger ) as uinteger
    'finds the next prime after n, excluding n if it happens to be prime itself
    if n = 0 then return 2
    if n < 3 then return n + 1
    dim as integer q = n + 2
    while not isprime(q)
        q+=2
    wend
    return q
end function

function lastprime( n as uinteger ) as uinteger
    'finds the last prime before n, excluding n if it happens to be prime itself
    if n = 2 then return 0       'zero isn't prime, but it is a good sentinel value :)
    if n = 3 then return 2
    dim as integer q = n - 2
    while not isprime(q)
        q-=2
    wend
    return q
end function

function isstrong( p as integer ) as boolean
    if nextprime(p) + lastprime(p) >= 2*p then return false else return true
end function

function isweak( p as integer ) as boolean
    if nextprime(p) + lastprime(p) <= 2*p then return false else return true
end function

print "The first 36 strong primes are: "
dim as uinteger c, p=3
while p < 10000000
    if isprime(p) andalso isstrong(p) then 
        c += 1
        if c <= 36 then print p;" ";
        if c=37 then print
    end if
    if p = 1000001 then print "There are ";c;" strong primes below one million" 
    p+=2
wend
print "There are ";c;" strong primes below ten million"
print
 
print "The first 37 weak primes are: "
p=3 : c=0
while p < 10000000
    if isprime(p) andalso isweak(p) then 
        c += 1
        if c <= 37 then print p;" ";
        if c=38 then print
    end if

    if p = 1000001 then print "There are ";c;" weak primes below one million" 
    p+=2
wend
print "There are ";c;" weak primes below ten million"
print
Output:

The first 36 strong primes are: 11 17 29 37 41 59 67 71 79 97 101 107 127 137 149 163 179 191 197 223 227 239 251 269 277 281 307 311 331 347 367 379 397 419 431 439 There are 37723 strong primes below one million There are 320991 strong primes below ten million

The first 37 weak primes are: 3 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181 193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401 There are 37780 weak primes below one million There are 321750 weak primes below ten million

Frink[edit]

strongPrimes[end=undef] := select[primes[3,end], {|p| p > (previousPrime[p] + nextPrime[p])/2 }] 
weakPrimes[end=undef]   := select[primes[3,end], {|p| p < (previousPrime[p] + nextPrime[p])/2 }] 

println["First 36 strong primes:  " + first[strongPrimes[], 36]]
println["Strong primes below  1,000,000: " + length[strongPrimes[1_000_000]]]
println["Strong primes below 10,000,000: " + length[strongPrimes[10_000_000]]]

println["First 37 weak primes:  " + first[weakPrimes[], 37]]
println["Weak primes below  1,000,000: " + length[weakPrimes[1_000_000]]]
println["Weak primes below 10,000,000: " + length[weakPrimes[10_000_000]]]
Output:
First 36 strong primes:  [11, 17, 29, 37, 41, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 163, 179, 191, 197, 223, 227, 239, 251, 269, 277, 281, 307, 311, 331, 347, 367, 379, 397, 419, 431, 439]
Strong primes below  1,000,000: 37723
Strong primes below 10,000,000: 320991
First 37 weak primes:  [3, 7, 13, 19, 23, 31, 43, 47, 61, 73, 83, 89, 103, 109, 113, 131, 139, 151, 167, 181, 193, 199, 229, 233, 241, 271, 283, 293, 313, 317, 337, 349, 353, 359, 383, 389, 401]
Weak primes below  1,000,000: 37780
Weak primes below 10,000,000: 321750

Go[edit]

package main

import "fmt"

func sieve(limit int) []bool {
    limit++
    // True denotes composite, false denotes prime.
    // Don't bother marking even numbers >= 4 as composite.
    c := make([]bool, limit)
    c[0] = true
    c[1] = true

    p := 3 // start from 3
    for {
        p2 := p * p
        if p2 >= limit {
            break
        }
        for i := p2; i < limit; i += 2 * p {
            c[i] = true
        }
        for {
            p += 2
            if !c[p] {
                break
            }
        }
    }
    return c
}

func commatize(n int) string {
    s := fmt.Sprintf("%d", n)
    le := len(s)
    for i := le - 3; i >= 1; i -= 3 {
        s = s[0:i] + "," + s[i:]
    }
    return s
}

func main() {
    // sieve up to 10,000,019 - the first prime after 10 million
    const limit = 1e7 + 19
    sieved := sieve(limit)
    // extract primes
    var primes = []int{2}
    for i := 3; i <= limit; i += 2 {
        if !sieved[i] {
            primes = append(primes, i)
        }
    }
    // extract strong and weak primes
    var strong []int
    var weak = []int{3}                  // so can use integer division for rest
    for i := 2; i < len(primes)-1; i++ { // start from 5
        if primes[i] > (primes[i-1]+primes[i+1])/2 {
            strong = append(strong, primes[i])
        } else if primes[i] < (primes[i-1]+primes[i+1])/2 {
            weak = append(weak, primes[i])
        }
    }

    fmt.Println("The first 36 strong primes are:")
    fmt.Println(strong[:36])
    count := 0
    for _, p := range strong {
        if p >= 1e6 {
            break
        }
        count++
    }
    fmt.Println("\nThe number of strong primes below 1,000,000 is", commatize(count))
    fmt.Println("\nThe number of strong primes below 10,000,000 is", commatize(len(strong)))

    fmt.Println("\nThe first 37 weak primes are:")
    fmt.Println(weak[:37])
    count = 0
    for _, p := range weak {
        if p >= 1e6 {
            break
        }
        count++
    }
    fmt.Println("\nThe number of weak primes below 1,000,000 is", commatize(count))
    fmt.Println("\nThe number of weak primes below 10,000,000 is", commatize(len(weak)))
}
Output:
The first 36 strong primes are:
[11 17 29 37 41 59 67 71 79 97 101 107 127 137 149 163 179 191 197 223 227 239 251 269 277 281 307 311 331 347 367 379 397 419 431 439]

The number of strong primes below 1,000,000 is 37,723

The number of strong primes below 10,000,000 is 320,991

The first 37 weak primes are:
[3 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181 193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401]

The number of weak primes below 1,000,000 is 37,780

The number of weak primes below 10,000,000 is 321,750

Haskell[edit]

Uses primes library: http://hackage.haskell.org/package/primes-0.2.1.0/docs/Data-Numbers-Primes.html

import Text.Printf (printf)
import Data.Numbers.Primes (primes)

xPrimes :: (Real a, Fractional b) => (b -> b -> Bool) -> [a] -> [a]
xPrimes op ps@(p1:p2:p3:xs)
  | realToFrac p2 `op` (realToFrac (p1 + p3) / 2) = p2 : xPrimes op (tail ps)
  | otherwise = xPrimes op (tail ps)

main :: IO ()
main = do 
  printf "First 36 strong primes: %s\n" . show . take 36 $ strongPrimes
  printf "Strong primes below 1,000,000: %d\n" . length . takeWhile (<1000000) $ strongPrimes
  printf "Strong primes below 10,000,000: %d\n\n" . length . takeWhile (<10000000) $ strongPrimes

  printf "First 37 weak primes: %s\n" . show . take 37 $ weakPrimes 
  printf "Weak primes below 1,000,000: %d\n" . length . takeWhile (<1000000) $ weakPrimes
  printf "Weak primes below 10,000,000: %d\n\n" . length . takeWhile (<10000000) $ weakPrimes
  where strongPrimes = xPrimes (>) primes
        weakPrimes   = xPrimes (<) primes
Output:
First 36 strong primes: [11,17,29,37,41,59,67,71,79,97,101,107,127,137,149,163,179,191,197,223,227,239,251,269,277,281,307,311,331,347,367,379,397,419,431,439]
Strong primes below 1,000,000: 37723
Strong primes below 10,000,000: 320991

First 37 weak primes: [3,7,13,19,23,31,43,47,61,73,83,89,103,109,113,131,139,151,167,181,193,199,229,233,241,271,283,293,313,317,337,349,353,359,383,389,401]
Weak primes below 1,000,000: 37780
Weak primes below 10,000,000: 321750

J[edit]

   Filter =: (#~`)(`:6)
   average =: +/ % #


   NB. vector of primes from 2 to 10000019
   PRIMES=:i.@>:&.(p:inv) 10000000


   strongQ =: 1&{ > [: average {. , {:
   STRONG_PRIMES=: (0, 0,~ 3&(strongQ\))Filter PRIMES
   NB. first 36 strong primes
   36 {. STRONG_PRIMES
11 17 29 37 41 59 67 71 79 97 101 107 127 137 149 163 179 191 197 223 227 239 251 269 277 281 307 311 331 347 367 379 397 419 431 439
   NB. tally of strong primes less than one and ten million
   +/ STRONG_PRIMES </ 1e6 * 1 10
37723 320991
   

   weakQ =: 1&{ < [: average {. , {:
   weaklings =: (0, 0,~ 3&(weakQ\))Filter PRIMES
   NB. first 37 weak primes   
   37 {. weaklings
3 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181 193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401
   NB. tally of weak primes less than one and ten million
   +/ weaklings </ 1e6 * 1 10
37780 321750

Java[edit]

public class StrongAndWeakPrimes {

    private static int MAX = 10_000_000 + 1000;
    private static boolean[] primes = new boolean[MAX];

    public static void main(String[] args) {
        sieve();
        System.out.println("First 36 strong primes:");        
        displayStrongPrimes(36);
        for ( int n : new int[] {1_000_000, 10_000_000}) {
            System.out.printf("Number of strong primes below %,d = %,d%n", n, strongPrimesBelow(n));
        }
        System.out.println("First 37 weak primes:");        
        displayWeakPrimes(37);
        for ( int n : new int[] {1_000_000, 10_000_000}) {
            System.out.printf("Number of weak primes below %,d = %,d%n", n, weakPrimesBelow(n));
        }
    }

    private static int weakPrimesBelow(int maxPrime) {
        int priorPrime = 2;
        int currentPrime = 3;
        int count = 0;
        while ( currentPrime < maxPrime ) {
            int nextPrime = getNextPrime(currentPrime);
            if ( currentPrime * 2 < priorPrime + nextPrime ) {
                count++;
            }
            priorPrime = currentPrime;
            currentPrime = nextPrime;
        }
        return count;
    }

    private static void displayWeakPrimes(int maxCount) {
        int priorPrime = 2;
        int currentPrime = 3;
        int count = 0;
        while ( count < maxCount ) {
            int nextPrime = getNextPrime(currentPrime);
            if ( currentPrime * 2 < priorPrime + nextPrime) {
                count++;
                System.out.printf("%d ", currentPrime);
            }
            priorPrime = currentPrime;
            currentPrime = nextPrime;
        }
        System.out.println();
    }

    private static int getNextPrime(int currentPrime) {
        int nextPrime = currentPrime + 2;
        while ( ! primes[nextPrime] ) {
            nextPrime += 2;
        }
        return nextPrime;
    }
    
    private static int strongPrimesBelow(int maxPrime) {
        int priorPrime = 2;
        int currentPrime = 3;
        int count = 0;
        while ( currentPrime < maxPrime ) {
            int nextPrime = getNextPrime(currentPrime);
            if ( currentPrime * 2 > priorPrime + nextPrime ) {
                count++;
            }
            priorPrime = currentPrime;
            currentPrime = nextPrime;
        }
        return count;
    }
    
    private static void displayStrongPrimes(int maxCount) {
        int priorPrime = 2;
        int currentPrime = 3;
        int count = 0;
        while ( count < maxCount ) {
            int nextPrime = getNextPrime(currentPrime);
            if ( currentPrime * 2 > priorPrime + nextPrime) {
                count++;
                System.out.printf("%d ", currentPrime);
            }
            priorPrime = currentPrime;
            currentPrime = nextPrime;
        }
        System.out.println();
    }

    private static final void sieve() {
        //  primes
        for ( int i = 2 ; i < MAX ; i++ ) {
            primes[i] = true;            
        }
        for ( int i = 2 ; i < MAX ; i++ ) {
            if ( primes[i] ) {
                for ( int j = 2*i ; j < MAX ; j += i ) {
                    primes[j] = false;
                }
            }
        }
    }

}
Output:
First 36 strong primes:
11 17 29 37 41 59 67 71 79 97 101 107 127 137 149 163 179 191 197 223 227 239 251 269 277 281 307 311 331 347 367 379 397 419 431 439 
Number of strong primes below 1,000,000 = 37,723
Number of strong primes below 10,000,000 = 320,991
First 37 weak primes:
3 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181 193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401 
Number of weak primes below 1,000,000 = 37,780
Number of weak primes below 10,000,000 = 321,750

jq[edit]

Works with: jq

Also works with gojq, the Go implementation of jq

The following assumes that `primes` generates a stream of primes less than or equal to `.` as defined, for example, at Sieve of Eratosthenes]].

def count(s): reduce s as $_ (0; .+1);

# Emit {strong, weak} primes up to and including $n
def strong_weak_primes:
   . as $n
   | primes as $primes
   | ("\nCheck: last prime generated: \($primes[-1])" | debug) as $debug
   | reduce range(1; $primes|length-1) as $p ({};
       (($primes[$p-1] + $primes[$p+1]) / 2) as $x
       | if $primes[$p] > $x
         then .strong += [$primes[$p]]
         elif $primes[$p] < $x 
         then .weak += [$primes[$p]]
	 else .
	 end );

(1e7 + 19)
  | strong_weak_primes as {$strong, $weak}
  | "The first 36 strong primes are:",
    $strong[:36],
  "\nThe count of the strong primes below 1e6: \(count($strong[]|select(. < 1e6 )))",
  "\nThe count of the strong primes below 1e7: \(count($strong[]|select(. < 1e7 )))",

  "\nThe first 37 weak primes are:",
  $weak[:37],
  "\nThe count of the weak primes below 1e6: \(count($weak[]|select(. < 1e6 )))",
  "\nThe count of the weak primes below 1e7: \(count($weak[]|select(. < 1e7 )))"
Output:
The first 36 strong primes are:
[11,17,29,37,41,59,67,71,79,97,101,107,127,137,149,163,179,191,197,223,227,239,251,269,277,281,307,311,331,347,367,379,397,419,431,439]

The count of the strong primes below 1e6: 37723

The count of the strong primes below 1e7: 320991

The first 37 weak primes are:
[3,7,13,19,23,31,43,47,61,73,83,89,103,109,113,131,139,151,167,181,193,199,229,233,241,271,283,293,313,317,337,349,353,359,383,389,401]

The count of the weak primes below 1e6: 37780

The count of the weak primes below 1e7: 321750

Julia[edit]

using Primes, Formatting

function parseprimelist()
    primelist = primes(2, 10000019)
    strongs = Vector{Int64}()
    weaks = Vector{Int64}()
    balanceds = Vector{Int64}()
    for (n, p) in enumerate(primelist)
        if n == 1 || n == length(primelist)
            continue
        end
        x = (primelist[n - 1] + primelist[n + 1]) / 2
        if x > p
            push!(weaks, p)
        elseif x < p 
            push!(strongs, p)
        else
            push!(balanceds, p)
        end
    end
    println("The first 36 strong primes are: ", strongs[1:36])
    println("There are ", format(sum(map(x -> x < 1000000, strongs)), commas=true), " stromg primes less than 1 million.")
    println("There are ", format(length(strongs), commas=true), " strong primes less than 10 million.")    
    println("The first 37 weak primes are: ", weaks[1:37])
    println("There are ", format(sum(map(x -> x < 1000000, weaks)), commas=true), " weak primes less than 1 million.")
    println("There are ", format(length(weaks), commas=true), " weak primes less than 10 million.")    
    println("The first 28 balanced primes are: ", balanceds[1:28])
    println("There are ", format(sum(map(x -> x < 1000000, balanceds)), commas=true), " balanced primes less than 1 million.")
    println("There are ", format(length(balanceds), commas=true), " balanced primes less than 10 million.")    
end

parseprimelist()
Output:

The first 36 strong primes are: [11, 17, 29, 37, 41, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 163, 179, 191, 197, 223, 227, 239, 251, 269, 277, 281, 307, 311, 331, 347, 367, 379, 397, 419, 431, 439] There are 37,723 stromg primes less than 1 million. There are 320,991 strong primes less than 10 million. The first 37 weak primes are: [3, 7, 13, 19, 23, 31, 43, 47, 61, 73, 83, 89, 103, 109, 113, 131, 139, 151, 167, 181, 193, 199, 229, 233, 241, 271, 283, 293, 313, 317, 337, 349, 353, 359, 383, 389, 401] There are 37,780 weak primes less than 1 million. There are 321,750 weak primes less than 10 million. The first 28 balanced primes are: [5, 53, 157, 173, 211, 257, 263, 373, 563, 593, 607, 653, 733, 947, 977, 1103, 1123, 1187, 1223, 1367, 1511, 1747, 1753, 1907, 2287, 2417, 2677, 2903] There are 2,994 balanced primes less than 1 million. There are 21,837 balanced primes less than 10 million.

Kotlin[edit]

Translation of: Java
private const val MAX = 10000000 + 1000
private val primes = BooleanArray(MAX)

fun main() {
    sieve()

    println("First 36 strong primes:")
    displayStrongPrimes(36)
    for (n in intArrayOf(1000000, 10000000)) {
        System.out.printf("Number of strong primes below %,d = %,d%n", n, strongPrimesBelow(n))
    }

    println("First 37 weak primes:")
    displayWeakPrimes(37)
    for (n in intArrayOf(1000000, 10000000)) {
        System.out.printf("Number of weak primes below %,d = %,d%n", n, weakPrimesBelow(n))
    }
}

private fun weakPrimesBelow(maxPrime: Int): Int {
    var priorPrime = 2
    var currentPrime = 3
    var count = 0
    while (currentPrime < maxPrime) {
        val nextPrime = getNextPrime(currentPrime)
        if (currentPrime * 2 < priorPrime + nextPrime) {
            count++
        }
        priorPrime = currentPrime
        currentPrime = nextPrime
    }
    return count
}

private fun displayWeakPrimes(maxCount: Int) {
    var priorPrime = 2
    var currentPrime = 3
    var count = 0
    while (count < maxCount) {
        val nextPrime = getNextPrime(currentPrime)
        if (currentPrime * 2 < priorPrime + nextPrime) {
            count++
            print("$currentPrime ")
        }
        priorPrime = currentPrime
        currentPrime = nextPrime
    }
    println()
}

private fun getNextPrime(currentPrime: Int): Int {
    var nextPrime = currentPrime + 2
    while (!primes[nextPrime]) {
        nextPrime += 2
    }
    return nextPrime
}

private fun strongPrimesBelow(maxPrime: Int): Int {
    var priorPrime = 2
    var currentPrime = 3
    var count = 0
    while (currentPrime < maxPrime) {
        val nextPrime = getNextPrime(currentPrime)
        if (currentPrime * 2 > priorPrime + nextPrime) {
            count++
        }
        priorPrime = currentPrime
        currentPrime = nextPrime
    }
    return count
}

private fun displayStrongPrimes(maxCount: Int) {
    var priorPrime = 2
    var currentPrime = 3
    var count = 0
    while (count < maxCount) {
        val nextPrime = getNextPrime(currentPrime)
        if (currentPrime * 2 > priorPrime + nextPrime) {
            count++
            print("$currentPrime ")
        }
        priorPrime = currentPrime
        currentPrime = nextPrime
    }
    println()
}

private fun sieve() { //  primes
    for (i in 2 until MAX) {
        primes[i] = true
    }
    for (i in 2 until MAX) {
        if (primes[i]) {
            var j = 2 * i
            while (j < MAX) {
                primes[j] = false
                j += i
            }
        }
    }
}
Output:
First 36 strong primes:
11 17 29 37 41 59 67 71 79 97 101 107 127 137 149 163 179 191 197 223 227 239 251 269 277 281 307 311 331 347 367 379 397 419 431 439 
Number of strong primes below 1,000,000 = 37,723
Number of strong primes below 10,000,000 = 320,991
First 37 weak primes:
3 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181 193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401 
Number of weak primes below 1,000,000 = 37,780
Number of weak primes below 10,000,000 = 321,750

Ksh[edit]

#!/bin/ksh

# Strong and weak primes
#	# Find and display (on one line) the first   36 strong  primes.
#	# Find and display the count of the strong primes below 1,000,000.
#	# Find and display the count of the strong primes below 10,000,000.
#	# Find and display (on one line) the first   37 weak  primes.
#	# Find and display the count of the weak primes below 1,000,000.
#	# Find and display the count of the weak primes below 10,000,000.
#	# (Optional) display the counts and "below numbers" with commas. ???

#	# A strong prime is when prime[p] > (prime[p-1] + prime[p+1]) ÷ 2
#	# A  weak prime  is when prime[p] < (prime[p-1] + prime[p+1]) ÷ 2
#	# Balanced prime is when prime[p] = (prime[p-1] + prime[p+1]) ÷ 2

#	# Variables:
#
integer  NUM_STRONG=36 NUM_WEAK=37 GOAL1=1000000 MAX_INT=10000000

#	# Functions:
#
#	# Function _isprime(n) return 1 for prime, 0 for not prime
#
function _isprime {
	typeset _n ; integer _n=$1
	typeset _i ; integer _i

	(( _n < 2 )) && return 0
	for (( _i=2 ; _i*_i<=_n ; _i++ )); do
		(( ! ( _n % _i ) )) && return 0
	done
	return 1
}

#	# Function _strength(prime[n], prime[n-1], prime[n+1]) return 1 for strong
#
function _strength {
	typeset _pri ; integer _pri=$1		# PRIme number under consideration
	typeset _pre ; integer _pre=$2		# PREvious prime number
	typeset _nex ; integer _nex=$3		# NEXt prime number
	typeset _result ; typeset -F1 _result

	(( _result = (_pre + _nex) / 2.0 ))
	(( _pri > _result )) && echo STRONG && return 0
	(( _pri < _result )) && echo WEAK   && return 1
	echo BALANCED && return 99
}

 #####
# main #
 ######

integer spcnt=0 wpcnt=0 bpcnt=0 sflg=0 wflg=0 i j k goal1_strong goal1_weak
typeset -C prime	# prime[].val  prime[].typ
	typeset -a prime.val
	typeset -a prime.typ
prime.typ[0]='NA' ; prime.typ[1]='NA'

for (( i=2; i<MAX_INT; i++ )); do
	_isprime ${i} ; (( ! $? )) && continue
	prime.val+=( ${i} )
	(( ${#prime.val[*]} <= 2 )) && continue

	(( j = ${#prime.val[*]} - 2 )) ; (( k = j - 1 ))
	prime.typ+=( $(_strength ${prime.val[${j}]} ${prime.val[k]} ${prime.val[-1]}) )
	case $? in
		 0)	(( spcnt++ ))
			(( spcnt <= NUM_STRONG )) && strbuff+="${prime.val[j]}, "
			(( i >= GOAL1 )) && (( ! sflg )) && (( goal1_strong = spcnt - 1 )) && (( sflg = 1 ))
		 ;;

		 1) (( wpcnt++ ))
			(( wpcnt <= NUM_WEAK )) && weabuff+="${prime.val[j]}, "
			(( i >= GOAL1 )) && (( ! wflg )) && (( goal1_weak = wpcnt - 1 )) && (( wflg = 1 ))
		 ;;

		99)	(( bpcnt++ ))
		 ;;
	esac
done

printf "Total primes under %d = %d\n\n"				$MAX_INT	${#prime.val[*]}
printf "First %d Strong Primes are: %s\n\n"			$NUM_STRONG	"${strbuff%,*}"
printf "Number of Strong Primes under %d  is: %d\n"		$GOAL1		${goal1_strong}
printf "Number of Strong Primes under %d is: %d\n\n\n"		$MAX_INT	${spcnt}
printf "First %d Weak Primes are: %s\n\n"			$NUM_WEAK	"${weabuff%,*}"
printf "Number of Weak Primes under %d  is: %d\n"		$GOAL1		${goal1_weak}
printf "Number of Weak Primes under %d is: %d\n\n\n"		$MAX_INT	${wpcnt}
printf "Number of Balanced Primes under %d is: %d\n\n\n"	$MAX_INT	${bpcnt}
Output:

Total primes under 10000000 = 664579

First 36 Strong Primes are: 11, 17, 29, 37, 41, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 163, 179, 191, 197, 223, 227, 239, 251, 269, 277, 281, 307, 311, 331, 347, 367, 379, 397, 419, 431, 439

Number of Strong Primes under 1000000 is: 37723 Number of Strong Primes under 10000000 is: 320991

First 37 Weak Primes are: 3, 7, 13, 19, 23, 31, 43, 47, 61, 73, 83, 89, 103, 109, 113, 131, 139, 151, 167, 181, 193, 199, 229, 233, 241, 271, 283, 293, 313, 317, 337, 349, 353, 359, 383, 389, 401

Number of Weak Primes under 1000000 is: 37779 Number of Weak Primes under 10000000 is: 321749

Number of Balanced Primes under 10000000 is: 21837


Lua[edit]

This could be made faster but favours readability. It runs in about 3.3 seconds in LuaJIT on a 2.8 GHz core.

-- Return a table of the primes up to n, then one more
function primeList (n)
  local function isPrime (x)
    for d = 3, math.sqrt(x), 2 do
      if x % d == 0 then return false end
    end
    return true
  end
  local pTable, j = {2, 3}
  for i = 5, n, 2 do
    if isPrime(i) then
      table.insert(pTable, i)
    end
    j = i
  end
  repeat j = j + 2 until isPrime(j)
  table.insert(pTable, j)
  return pTable
end

-- Return a boolean indicating whether prime p is strong
function isStrong (p)
  if p == 1 or p == #prime then return false end
  return prime[p] > (prime[p-1] + prime[p+1]) / 2 
end

-- Return a boolean indicating whether prime p is weak
function isWeak (p)
  if p == 1 or p == #prime then return false end
  return prime[p] < (prime[p-1] + prime[p+1]) / 2 
end

-- Main procedure
prime = primeList(1e7)
local strong, weak, sCount, wCount = {}, {}, 0, 0
for k, v in pairs(prime) do
  if isStrong(k) then
    table.insert(strong, v)
    if v < 1e6 then sCount = sCount + 1 end
  end
  if isWeak(k) then
    table.insert(weak, v)
    if v < 1e6 then wCount = wCount + 1 end
  end
end
print("The first 36 strong primes are:")
for i = 1, 36 do io.write(strong[i] .. " ") end
print("\n\nThere are " .. sCount .. " strong primes below one million.")
print("\nThere are " .. #strong .. " strong primes below ten million.")
print("\nThe first 37 weak primes are:")
for i = 1, 37 do io.write(weak[i] .. " ") end
print("\n\nThere are " .. wCount .. " weak primes below one million.")
print("\nThere are " .. #weak .. " weak primes below ten million.")
Output:
The first 36 strong primes are:
11 17 29 37 41 59 67 71 79 97 101 107 127 137 149 163 179 191 197 223 227 239 251 269 277 281 307 311 331 347 367 379 397 419 431 439

There are 37723 strong primes below one million.

There are 320991 strong primes below ten million.

The first 37 weak primes are:
3 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181 193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401

There are 37780 weak primes below one million.

There are 321750 weak primes below ten million.

Maple[edit]

isStrong := proc(n::posint) local holder; 
holder := false; 
if isprime(n) and 1/2*prevprime(n) + 1/2*nextprime(n) < n then 
   holder := true; 
end if; 
return holder; 
end proc:

isWeak := proc(n::posint) local holder; 
holder := false; 
if isprime(n) and n < 1/2*prevprime(n) + 1/2*nextprime(n) then 
   holder := true; 
end if; 
return holder; 
end proc

findStrong := proc(n::posint) local count, list, k; 
count := 0; list := []; 
for k from 3 while count < n do 
  if isStrong(k) then count := count + 1; 
    list := [op(list), k]; 
  end if; 
end do; 
return list; 
end proc:

findWeak := proc(n::posint) local count, list, k; 
count := 0; 
list := []; 
for k from 3 while count < n do 
  if isWeak(k) then 
     count := count + 1; 
     list := [op(list), k]; 
  end if; 
end do; 
return list; 
end proc:

findStrong(36)
findWeak(37)
countStrong(1000000)
countStrong(10000000)
countWeak(1000000)
countWeak(10000000)
Output:
[11, 17, 29, 37, 41, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 163, 179, 191, 197, 223, 227, 239, 251, 269, 277, 281, 307, 311, 331, 347, 367, 379, 397, 419, 431, 439]
[3, 7, 13, 19, 23, 31, 43, 47, 61, 73, 83, 89, 103, 109, 113, 131, 139, 151, 167, 181, 193, 199, 229, 233, 241, 271, 283, 293, 313, 317, 337, 349, 353, 359, 383, 389, 401]
37723
320991
37780
321750

Mathematica/Wolfram Language[edit]

p = Prime[Range[PrimePi[10^3]]];
SequenceCases[p, ({a_, b_, c_}) /; (a + c < 2 b) :> b, 36, Overlaps -> True]
SequenceCases[p, ({a_, b_, c_}) /; (a + c > 2 b) :> b, 37, Overlaps -> True]
p = Prime[Range[PrimePi[10^6] + 1]];
Length[Select[Partition[p, 3, 1], #[[3]] + #[[1]] < 2 #[[2]] &]]
Length[Select[Partition[p, 3, 1], #[[3]] + #[[1]] > 2 #[[2]] &]]
p = Prime[Range[PrimePi[10^7] + 1]];
Length[Select[Partition[p, 3, 1], #[[3]] + #[[1]] < 2 #[[2]] &]]
Length[Select[Partition[p, 3, 1], #[[3]] + #[[1]] > 2 #[[2]] &]]
Output:
{11,17,29,37,41,59,67,71,79,97,101,107,127,137,149,163,179,191,197,223,227,239,251,269,277,281,307,311,331,347,367,379,397,419,431,439}
{3,7,13,19,23,31,43,47,61,73,83,89,103,109,113,131,139,151,167,181,193,199,229,233,241,271,283,293,313,317,337,349,353,359,383,389,401}
37723
37780
320991
321750


Nim[edit]

import math, strutils

const
  M = 10_000_000
  N = M + 19      # Maximum value for sieve.

# Fill sieve of Erathosthenes.
var comp: array[2..N, bool]   # True means composite; default is prime.
for n in countup(3, sqrt(N.toFloat).int, 2):
  if not comp[n]:
    for k in countup(n * n, N, 2 * n):
      comp[k] = true

# Build list of primes.
var primes = @[2]
for n in countup(3, N, 2):
  if not comp[n]:
    primes.add n
if primes[^1] < M: quit "Not enough primes: please, increase value of N."

# Build lists of strong and weak primes.
var strongPrimes, weakPrimes: seq[int]
for i in 1..<primes.high:
  let p = primes[i]
  if p shl 1 > primes[i - 1] + primes[i + 1]:
    strongPrimes.add p
  elif p shl 1 < primes[i - 1] + primes[i + 1]:
    weakPrimes.add p


when isMainModule:

  proc count(list: seq[int]; max: int): int =
    ## Return the count of values less than "max".
    for p in list:
      if p >= max: break
      inc result

  echo "First 36 strong primes:"
  echo "  ", strongPrimes[0..35].join(" ")
  echo "Count of strong primes below 1_000_000: ", strongPrimes.count(1_000_000)
  echo "Count of strong primes below 10_000_000: ", strongPrimes.count(10_000_000)
  echo()

  echo "First 37 weak primes:"
  echo "  ", weakPrimes[0..36].join(" ")
  echo "Count of weak primes below 1_000_000: ", weakPrimes.count(1_000_000)
  echo "Count of weak primes below 10_000_000: ", weakPrimes.count(10_000_000)
Output:
First 36 strong primes:
  11 17 29 37 41 59 67 71 79 97 101 107 127 137 149 163 179 191 197 223 227 239 251 269 277 281 307 311 331 347 367 379 397 419 431 439
Count of strong primes below 1_000_000: 37723
Count of strong primes below 10_000_000: 320991

First 37 weak primes:
  3 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181 193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401
Count of weak primes below 1_000_000: 37780
Count of weak primes below 10_000_000: 321750

Pascal[edit]

Converting the primes into deltaPrime, so that its easy to check the strong- /weakness. Startprime 2 +1 -> (3)+2-> (5)+2 ->(7) +4-> (11)+2 .... 1,2,2,4,2,4,2,4,6,2,.... By using only odd primes startprime is 3 and delta -> delta/2

If deltaAfter < deltaBefore than a strong prime is found.

program WeakPrim;
{$IFNDEF FPC}
  {$AppType CONSOLE}
{$ENDIF}
const
  PrimeLimit = 1000*1000*1000;//must be >= 2*3;
type
  tLimit = 0..(PrimeLimit-1) DIV 2;
  tPrimCnt = 0..51*1000*1000;  
  tWeakStrong = record
                   strong,
                   balanced,
                   weak : NativeUint;
                end;   
var
  primes: array [tLimit] of byte; //always initialized with 0 at startup
  delta : array [tPrimCnt] of byte;
  cntWS : tWeakStrong;  
  deltaCnt :NativeUint;
  
procedure sieveprimes;
//Only odd numbers, minimal count of strikes
var
  spIdx,sieveprime,sievePos,fact :NativeUInt;
begin
  spIdx := 1;
  repeat
    if primes[spIdx]=0 then
    begin
      sieveprime := 2*spIdx+1;
      fact := PrimeLimit DIV sieveprime;
      if Not(odd(fact)) then
        dec(fact);
      IF fact < sieveprime then
        BREAK;
      sievePos := ((fact*sieveprime)-1) DIV 2;
      fact := (fact-1) DIV 2;
      repeat
        primes[sievePos] := 1;
        repeat
          dec(fact);
          dec(sievePos,sieveprime);
        until primes[fact]= 0;
      until fact < spIdx;
    end;
    inc(spIdx);
  until false;
end;  
{ Not neccessary for this small primes.
procedure EmergencyStop(i:NativeInt);
Begin
  Writeln( 'STOP at ',i,'.th prime');
  HALT(i);
end;    
}
function GetDeltas:NativeUint;
//Converting prime positions into distance  
var 
  i,j,last : NativeInt;
Begin
  j :=0;
  i := 1;
  last :=1;
  For i := 1 to High(primes) do
    if primes[i] = 0 then
    Begin
      //IF i-last > 255 {aka delta prim > 512} then  EmergencyStop (j);
      delta[j] := i-last;
      last := i;
      inc(j);
   end;
   GetDeltas := j;
end;  
 
procedure OutHeader;
Begin
  writeln('Limit':12,'Strong':10,'balanced':12,'weak':10);
end;     

procedure OutcntWS (const cntWS : tWeakStrong;Lmt:NativeInt);
Begin
  with cntWS do
    writeln(lmt:12,Strong:10,balanced:12,weak:10);
end;     

procedure CntWeakStrong10(var Out:tWeakStrong);
// Output a table of values for strang/balanced/weak for 10^n 
var
  idx,diff,prime,lmt :NativeInt;
begin 
  OutHeader;
  lmt := 10;
  fillchar(Out,SizeOf(Out),#0);
  idx := 0;
  prime:=3;
  repeat
    dec(prime,2*delta[idx]);  
    while idx < deltaCnt do   
    Begin
      inc(prime,2*delta[idx]);
      IF prime > lmt then 
         BREAK;
         
      diff := delta[idx] - delta[idx+1];
      if diff>0 then 
        inc(Out.strong)
      else  
        if diff< 0 then 
          inc(Out.weak)
        else
          inc(Out.balanced);
          
      inc(idx);            
    end; 
    OutcntWS(Out,Lmt);
    lmt := lmt*10;
  until Lmt >  PrimeLimit; 
end;

procedure WeakOut(cnt:NativeInt);
var   
  idx,prime : NativeInt;
begin 
  Writeln('The first ',cnt,' weak primes');
  prime:=3;      
  idx := 0;
  repeat
    inc(prime,2*delta[idx]);  
    if delta[idx] - delta[idx+1]< 0 then
    Begin 
      write(prime,' ');
      dec(cnt);
      IF cnt <=0 then
        BREAK;
    end; 
    inc(idx);   
  until idx >= deltaCnt;
  Writeln;
end;

procedure StrongOut(cnt:NativeInt);
var   
  idx,prime : NativeInt;
begin 
  Writeln('The first ',cnt,' strong primes');
  prime:=3;      
  idx := 0;
  repeat
    inc(prime,2*delta[idx]);  
    if delta[idx] - delta[idx+1]> 0 then
    Begin 
      write(prime,' ');
      dec(cnt);
      IF cnt <=0 then
        BREAK;
    end; 
    inc(idx);   
  until idx >= deltaCnt;
  Writeln;
end;

begin
  sieveprimes;
  deltaCnt := GetDeltas;  
  
  StrongOut(36);
  WeakOut(37);
  CntWeakStrong10(CntWs);
end.
Output:
The first 36 strong primes
11 17 29 37 41 59 67 71 79 97 101 107 127 137 149 163 179 191 197 223 227 239 251 269 277 281 307 311 331 347 367 379 397 419 431 439 
The first 37 weak primes
3 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181 193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401 
       Limit    Strong    balanced      weak
          10         0           1         2
         100        10           2        12
        1000        73          15        79
       10000       574          65       589
      100000      4543         434      4614
     1000000     37723        2994     37780
    10000000    320991       21837    321750
   100000000   2796946      167032   2797476
  1000000000  24758535     1328401  24760597

real    0m3.011s

Perl[edit]

Translation of: Raku
Library: ntheory
use ntheory qw(primes vecfirst);

sub comma {
    (my $s = reverse shift) =~ s/(.{3})/$1,/g;
    $s =~ s/,(-?)$/$1/;
    $s = reverse $s;
}

sub below { my ($m, @a) = @_; vecfirst { $a[$_] > $m } 0..$#a }

my (@strong, @weak, @balanced);
my @primes = @{ primes(10_000_019) };

for my $k (1 .. $#primes - 1) {
    my $x = ($primes[$k - 1] + $primes[$k + 1]) / 2;
    if    ($x > $primes[$k]) { push @weak,     $primes[$k] }
    elsif ($x < $primes[$k]) { push @strong,   $primes[$k] }
    else                     { push @balanced, $primes[$k] }
}

for ([\@strong,   'strong',   36, 1e6, 1e7],
     [\@weak,     'weak',     37, 1e6, 1e7],
     [\@balanced, 'balanced', 28, 1e6, 1e7]) {
    my($pr, $type, $d, $c1, $c2) = @$_;
    print "\nFirst $d $type primes:\n", join ' ', map { comma $_ } @$pr[0..$d-1], "\n";
    print "Count of $type primes <=  @{[comma $c1]}:  " . comma below($c1,@$pr) . "\n";
    print "Count of $type primes <= @{[comma $c2]}: "   . comma scalar @$pr . "\n";
}
Output:
First 36 strong primes:
11 17 29 37 41 59 67 71 79 97 101 107 127 137 149 163 179 191 197 223 227 239 251 269 277 281 307 311 331 347 367 379 397 419 431 439 
Count of strong primes <=  1,000,000:  37,723
Count of strong primes <= 10,000,000: 320,991

First 37 weak primes:
3 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181 193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401 
Count of weak primes <=  1,000,000:  37,780
Count of weak primes <= 10,000,000: 321,750

First 28 balanced primes:
5 53 157 173 211 257 263 373 563 593 607 653 733 947 977 1,103 1,123 1,187 1,223 1,367 1,511 1,747 1,753 1,907 2,287 2,417 2,677 2,903 
Count of balanced primes <=  1,000,000:  2,994
Count of balanced primes <= 10,000,000: 21,837

Phix[edit]

with javascript_semantics
sequence strong = {}, weak = {}
for i=2 to get_maxprime(1e14) do -- (ie idx of primes < (sqrt(1e14)==1e7), bar 1st)
    integer p = get_prime(i),
    c = compare(p,(get_prime(i-1)+get_prime(i+1))/2)
    if c=+1 then strong &= p end if
    if c=-1 then weak   &= p end if
end for
printf(1,"The first thirty six strong primes: %s\n",{join(shorten(strong[1..36],"",4,"%2d"),", ")})
printf(1,"The first thirty seven weak primes: %s\n",{join(shorten(  weak[1..37],"",4,"%2d"),", ")})
printf(1,"There are %,d strong primes below %,d and %,d below %,d\n",{abs(binary_search(1e6,strong))-1,1e6,length(strong),1e7})
printf(1,"There are %,d   weak primes below %,d and %,d below %,d\n",{abs(binary_search(1e6,  weak))-1,1e6,length(  weak),1e7})
Output:
The first thirty six strong primes: 11, 17, 29, 37, ..., 397, 419, 431, 439
The first thirty seven weak primes:  3,  7, 13, 19, ..., 359, 383, 389, 401
There are 37,723 strong primes below 1,000,000 and 320,991 below 10,000,000
There are 37,780   weak primes below 1,000,000 and 321,750 below 10,000,000

PureBasic[edit]

#MAX=10000000+20
Global Dim P.b(#MAX) : FillMemory(@P(),#MAX,1,#PB_Byte)
Global NewList Primes.i()
Global NewList Strong.i()
Global NewList Weak.i()

For n=2 To Sqr(#MAX)+1 : If P(n) : m=n*n : While m<=#MAX : P(m)=0 : m+n : Wend : EndIf : Next
For i=2 To #MAX : If p(i) : AddElement(Primes()) : Primes()=i : EndIf : Next

If FirstElement(Primes())
  pp=Primes()
  While NextElement(Primes())
    ap=Primes()
    If NextElement(Primes()) : np=Primes() : Else : Break : EndIf
    If ap>(pp+np)/2.0 : AddElement(Strong()) : Strong()=ap : If ap<1000000 : c1+1 : EndIf : EndIf
    If ap<(pp+np)/2.0 : AddElement(Weak()) : Weak()=ap : If ap<1000000 : c2+1 : EndIf : EndIf    
    PreviousElement(Primes()) : pp=Primes()
  Wend
EndIf

OpenConsole()
If FirstElement(Strong())
  PrintN("First 36 strong primes:")
  Print(Str(Strong())+" ")
  For i=2 To 36 : If NextElement(Strong()) : Print(Str(Strong())+" ") : Else : Break : EndIf : Next
  PrintN("")
EndIf
PrintN("Number of strong primes below  1'000'000 = "+FormatNumber(c1,0,".","'"))
PrintN("Number of strong primes below 10'000'000 = "+FormatNumber(ListSize(Strong()),0,".","'"))
If FirstElement(Weak())
  PrintN("First 37 weak primes:")
  Print(Str(Weak())+" ")
  For i=2 To 37 : If NextElement(Weak()) : Print(Str(Weak())+" ") : Else : Break : EndIf : Next
  PrintN("")
EndIf
PrintN("Number of weak primes below  1'000'000 = "+FormatNumber(c2,0,".","'")) 
PrintN("Number of weak primes below 10'000'000 = "+FormatNumber(ListSize(Weak()),0,".","'")) 
Input()
Output:
First 36 strong primes:
11 17 29 37 41 59 67 71 79 97 101 107 127 137 149 163 179 191 197 223 227 239 251 269 277 281 307 311 331 347 367 379 397 419 431 439 
Number of strong primes below  1'000'000 = 37'723
Number of strong primes below 10'000'000 = 320'991
First 37 weak primes:
3 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181 193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401 
Number of weak primes below  1'000'000 = 37'780
Number of weak primes below 10'000'000 = 321'750

Python[edit]

Using the popular numpy library for fast prime generation.

COmputes and shows the requested output then adds similar output for the "balanced" case where prime(p) == [prime(p-1) + prime(p+1)] ÷ 2.

import numpy as np

def primesfrom2to(n):
    # https://stackoverflow.com/questions/2068372/fastest-way-to-list-all-primes-below-n-in-python/3035188#3035188
    """ Input n>=6, Returns a array of primes, 2 <= p < n """
    sieve = np.ones(n//3 + (n%6==2), dtype=np.bool)
    sieve[0] = False
    for i in range(int(n**0.5)//3+1):
        if sieve[i]:
            k=3*i+1|1
            sieve[      ((k*k)//3)      ::2*k] = False
            sieve[(k*k+4*k-2*k*(i&1))//3::2*k] = False
    return np.r_[2,3,((3*np.nonzero(sieve)[0]+1)|1)]

p = primes10m   = primesfrom2to(10_000_000)
s = strong10m   = [t for s, t, u in zip(p, p[1:], p[2:]) 
                   if t > (s + u) / 2]
w = weak10m     = [t for s, t, u in zip(p, p[1:], p[2:]) 
                   if t < (s + u) / 2]
b = balanced10m = [t for s, t, u in zip(p, p[1:], p[2:]) 
                   if t == (s + u) / 2]

print('The first   36   strong primes:', s[:36])
print('The   count   of the strong primes below   1,000,000:',
      sum(1 for p in s if p < 1_000_000))
print('The   count   of the strong primes below  10,000,000:', len(s))
print('\nThe first   37   weak primes:', w[:37])
print('The   count   of the weak   primes below   1,000,000:',
      sum(1 for p in w if p < 1_000_000))
print('The   count   of the weak   primes below  10,000,000:', len(w))
print('\n\nThe first   10 balanced primes:', b[:10])
print('The   count   of balanced   primes below   1,000,000:',
      sum(1 for p in b if p < 1_000_000))
print('The   count   of balanced   primes below  10,000,000:', len(b))
print('\nTOTAL primes below   1,000,000:',
      sum(1 for pr in p if pr < 1_000_000))
print('TOTAL primes below  10,000,000:', len(p))
Output:
The first   36   strong primes: [11, 17, 29, 37, 41, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 163, 179, 191, 197, 223, 227, 239, 251, 269, 277, 281, 307, 311, 331, 347, 367, 379, 397, 419, 431, 439]
The   count   of the strong primes below   1,000,000: 37723
The   count   of the strong primes below  10,000,000: 320991

The first   37   weak primes: [3, 7, 13, 19, 23, 31, 43, 47, 61, 73, 83, 89, 103, 109, 113, 131, 139, 151, 167, 181, 193, 199, 229, 233, 241, 271, 283, 293, 313, 317, 337, 349, 353, 359, 383, 389, 401]
The   count   of the weak   primes below   1,000,000: 37780
The   count   of the weak   primes below  10,000,000: 321749


The first   10 balanced primes: [5, 53, 157, 173, 211, 257, 263, 373, 563, 593]
The   count   of balanced   primes below   1,000,000: 2994
The   count   of balanced   primes below  10,000,000: 21837

TOTAL primes below   1,000,000: 78498
TOTAL primes below  10,000,000: 664579

Raku[edit]

(formerly Perl 6)

Works with: Rakudo version 2018.11
sub comma { $^i.flip.comb(3).join(',').flip }

use Math::Primesieve;

my $sieve = Math::Primesieve.new;

my @primes = $sieve.primes(10_000_019);

my (@weak, @balanced, @strong);

for 1 ..^ @primes - 1 -> $p {
    given (@primes[$p - 1] + @primes[$p + 1]) / 2 {
        when * > @primes[$p] {     @weak.push: @primes[$p] }
        when * < @primes[$p] {   @strong.push: @primes[$p] }
        default              { @balanced.push: @primes[$p] }
    }
}

for @strong,   'strong',   36,
    @weak,     'weak',     37,
    @balanced, 'balanced', 28
  -> @pr, $type, $d {
    say "\nFirst $d $type primes:\n", @pr[^$d]».&comma;
    say "Count of $type primes <=  {comma 1e6}:  ", comma +@pr[^(@pr.first: * > 1e6,:k)];
    say "Count of $type primes <= {comma 1e7}: ", comma +@pr;
}
Output:
First 36 strong primes:
(11 17 29 37 41 59 67 71 79 97 101 107 127 137 149 163 179 191 197 223 227 239 251 269 277 281 307 311 331 347 367 379 397 419 431 439)
Count of strong primes <=  1,000,000:  37,723
Count of strong primes <= 10,000,000: 320,991

First 37 weak primes:
(3 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181 193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401)
Count of weak primes <=  1,000,000:  37,780
Count of weak primes <= 10,000,000: 321,750

First 28 balanced primes:
(5 53 157 173 211 257 263 373 563 593 607 653 733 947 977 1,103 1,123 1,187 1,223 1,367 1,511 1,747 1,753 1,907 2,287 2,417 2,677 2,903)
Count of balanced primes <=  1,000,000:  2,994
Count of balanced primes <= 10,000,000: 21,837

REXX[edit]

/*REXX program lists a sequence  (or a count)  of  ──strong──   or   ──weak──   primes. */
parse arg N kind _ . 1 . okind;     upper kind   /*obtain optional arguments from the CL*/
if N=='' | N==","  then N= 36                    /*Not specified?   Then assume default.*/
if kind=='' | kind==","  then kind= 'STRONG'     /* "      "          "     "      "    */
if _\==''                             then call ser 'too many arguments specified.'
if kind\=='WEAK'  &  kind\=='STRONG'  then call ser 'invalid 2nd argument: '   okind
if kind =='WEAK'  then weak= 1;  else weak= 0    /*WEAK  is a binary value for function.*/
w = linesize() - 1                               /*obtain the usable width of the term. */
tell= (N>0);    @.=;    N= abs(N)                /*N is negative?   Then don't display. */
!.=0;   !.1=2;  !.2=3;  !.3=5;  !.4=7;  !.5=11;  !.6=13;  !.7=17;  !.8=19;   !.9=23;  #= 8
@.='';  @.2=1;  @.3=1;  @.5=1;  @.7=1;  @.11=1;  @.13=1;  @.17=1;  @.19=1;   start= # + 1
m= 0;                           lim= 0           /*#  is the number of low primes so far*/
$=;     do i=3  for #-2   while lim<=N           /* [↓]  find primes, and maybe show 'em*/
        call strongWeak i-1;       $= strip($)   /*go see if other part of a KIND prime.*/
        end   /*i*/                              /* [↑]  allows faster loop (below).    */
                                                 /* [↓]  N:  default lists up to 35 #'s.*/
   do j=!.#+2  by 2  while  lim<N                /*continue on with the next odd prime. */
   if j // 3 == 0  then iterate                  /*is this integer a multiple of three? */
   parse var  j    ''  -1  _                     /*obtain the last decimal digit of  J  */
   if _      == 5  then iterate                  /*is this integer a multiple of five?  */
   if j // 7 == 0  then iterate                  /* "   "     "    "     "     " seven? */
   if j //11 == 0  then iterate                  /* "   "     "    "     "     " eleven?*/
   if j //13 == 0  then iterate                  /* "   "     "    "     "     "  13 ?  */
   if j //17 == 0  then iterate                  /* "   "     "    "     "     "  17 ?  */
   if j //19 == 0  then iterate                  /* "   "     "    "     "     "  19 ?  */
                                                 /* [↓]  divide by the primes.   ___    */
            do k=start  to #  while !.k * !.k<=j /*divide  J  by other primes ≤ √ J     */
            if j // !.k ==0   then iterate j     /*÷ by prev. prime?  ¬prime     ___    */
            end   /*k*/                          /* [↑]   only divide up to     √ J     */
   #= # + 1                                      /*bump the count of number of primes.  */
   !.#= j;                     @.j= 1            /*define a prime  and  its index value.*/
   call strongWeak #-1                           /*go see if other part of a KIND prime.*/
   end   /*j*/
                                                 /* [↓]  display number of primes found.*/
if $\==''  then say $                            /*display any residual primes in $ list*/
say
if tell  then say commas(m)' '     kind    "primes found."
         else say commas(m)' '     kind    "primes found below or equal to "    commas(N).
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
add: m= m+1; lim= m; if \tell & y>N  then do; lim= y; m= m-1; end; else call app; return 1
app: if tell  then if length($ y)>w  then do;  say $; $= y;   end; else $= $ y;   return 1
ser: say;  say;  say '***error***' arg(1);  say;  say;  exit 13   /*tell error message. */
commas: parse arg _;  do jc=length(_)-3  to 1  by -3; _=insert(',', _, jc); end;  return _
/*──────────────────────────────────────────────────────────────────────────────────────*/
strongWeak: parse arg x;  Lp= x - 1;     Hp= x + 1;     y=!.x;        s= (!.Lp + !.Hp) / 2
            if weak  then if y<s  then return add()               /*is  a    weak prime.*/
                                  else return 0                   /*not "      "    "   */
                     else if y>s  then return add()               /*is  an strong prime.*/
                                       return 0                   /*not  "   "      "   */

This REXX program makes use of   LINESIZE   REXX program (or BIF) which is used to determine the screen width (or linesize) of the terminal (console).   Some REXXes don't have this BIF.

The   LINESIZE.REX   REXX program is included here   ───►   LINESIZE.REX.


output   when using the default input of:     36   strong
11 17 29 37 41 59 67 71 79 97 101 107 127 137 149 163 179 191 197 223 227 239 251 269 277 281 307 311 331 347 367 379 397 419 431 439

36  STRONG primes found.
output   when using the default input of:     -1000000   strong
37,723  STRONG primes found below or equal to  1,000,000.
output   when using the default input of:     -10000000   strong
320,991  STRONG primes found below or equal to  10,000,000.
output   when using the default input of:     37   weak
3 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181 193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401

37  WEAK primes found.
output   when using the default input of:     -1000000   weak
37,780  WEAK primes found below or equal to  1,000,000.
output   when using the default input of:     -10000000   weak
321,750  WEAK primes found below or equal to  10,000,000.

Ring[edit]

load "stdlib.ring"

see "working..." + nl

p = 0
num = 0
pr1 = 37
pr2 = 38
limit1 = 457
limit2 = 1000000
limit3 = 10000000
primes = []

see "first 36 strong primes:" + nl
while true 
      p = p + 1
      if isprime(p)
         if p < limit1 
            add(primes,p)
         else
            exit
         ok
      ok
end

ln = len(primes)
for n = 2 to ln-1
    tmp = (primes[n-1] + primes[n+1])/2
    if primes[n] > tmp
       num = num + 1
       if num < pr1
          see " " + primes[n]
       ok
    ok
next

see nl + "first 37 weak primes:" + nl

num = 0
ln = len(primes)
for n = 2 to ln-1
    tmp = (primes[n-1] + primes[n+1])/2
    if primes[n] < tmp
       num = num + 1
       if num < pr2
          see " " + primes[n]
       ok
    ok
next

p = 0
primes = []
while true 
      p = p + 1
      if isprime(p)
         if p < limit3 
            add(primes,p)
         else
            exit
         ok
      ok
end

primes2 = 0
primes3 = 0
ln = len(primes)
for n = 2 to ln-1
    tmp = (primes[n-1] + primes[n+1])/2
    if primes[n] > tmp
       if primes[n] < limit2
          primes2 = primes2 + 1
       ok
       if primes[n] < limit3
          primes3 = primes3 + 1
       else
          exit
       ok
    ok
next

see nl
see "strong primes below 1,000,000: " + primes2 + nl
see "strong primes below 10,000,000: " + primes3 + nl

primes2 = 0
primes3 = 0
ln = len(primes)
for n = 2 to ln-1
    tmp = (primes[n-1] + primes[n+1])/2
    if primes[n] < tmp
       if primes[n] < limit2
          primes2 = primes2 + 1
       ok
       if primes[n] < limit3
          primes3 = primes3 + 1
       else
          exit
       ok
    ok
next

see nl
see "weak primes below 1,000,000: " + primes2 + nl
see "weak primes below 10,000,000: " + primes3 + nl

Output:

first 36 strong primes:
11 17 29 37 41 59 67 71 79 97 101 107 127 137 149 163 179 191 197 223 227 239 251 269 277 281 307 311 331 347 367 379 397 419 431 439
first 37   weak primes:
3 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181 193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401
strong primes below   1,000,000: 37723
strong primes below  10,000,000: 320991
weak primes below   1,000,000: 37780
weak primes below  10,000,000: 321750

Ruby[edit]

require 'prime'

strong_gen = Enumerator.new{|y| Prime.each_cons(3){|a,b,c|y << b if a+c-b<b} }
weak_gen   = Enumerator.new{|y| Prime.each_cons(3){|a,b,c|y << b if a+c-b>b} }

puts "First 36 strong primes:"
puts strong_gen.take(36).join(" "), "\n"
puts "First 37 weak primes:"
puts weak_gen.take(37).join(" "), "\n"

[1_000_000, 10_000_000].each do |limit|
  strongs, weaks = 0, 0
  Prime.each_cons(3) do |a,b,c|
    strongs += 1 if b > a+c-b
    weaks += 1 if b < a+c-b
    break if c > limit
  end
  puts "#{strongs} strong primes and #{weaks} weak primes below #{limit}."
end
Output:
First 36 strong primes:
11 17 29 37 41 59 67 71 79 97 101 107 127 137 149 163 179 191 197 223 227 239 251 269 277 281 307 311 331 347 367 379 397 419 431 439

First 37 weak primes:
3 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181 193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401

37723 strong primes and 37780 weak primes below 1000000.
320991 strong primes and 321750 weak primes below 10000000.

Rust[edit]

fn is_prime(n: i32) -> bool {
	for i in 2..n {
		if i * i > n {
			return true;
		}
		if n % i == 0 {
			return false;
		}
	}
	n > 1
}

fn next_prime(n: i32) -> i32 {
	for i in (n+1).. {
		if is_prime(i) {
			return i;
		}
	}
	0
}

fn main() {
	let mut n = 0;
	let mut prime_q = 5;
	let mut prime_p = 3;
	let mut prime_o = 2;

	print!("First 36 strong primes: ");
	while n < 36 {
		if prime_p > (prime_o + prime_q) / 2 {
			print!("{} ",prime_p);
			n += 1;
		}
		prime_o = prime_p;
		prime_p = prime_q;
		prime_q = next_prime(prime_q);
	}
	println!("");

	while prime_p < 1000000 {
		if prime_p > (prime_o + prime_q) / 2 {
			n += 1;
		}
		prime_o = prime_p;
		prime_p = prime_q;
		prime_q = next_prime(prime_q);
	}
	println!("strong primes below 1,000,000: {}", n);

	while prime_p < 10000000 {
		if prime_p > (prime_o + prime_q) / 2 {
			n += 1;
		}
		prime_o = prime_p;
		prime_p = prime_q;
		prime_q = next_prime(prime_q);
	}
	println!("strong primes below 10,000,000: {}", n);

	n = 0;
	prime_q = 5;
	prime_p = 3;
	prime_o = 2;

	print!("First 36 weak primes: ");
	while n < 36 {
		if prime_p < (prime_o + prime_q) / 2 {
			print!("{} ",prime_p);
			n += 1;
		}
		prime_o = prime_p;
		prime_p = prime_q;
		prime_q = next_prime(prime_q);
	}
	println!("");

	while prime_p < 1000000 {
		if prime_p < (prime_o + prime_q) / 2 {
			n += 1;
		}
		prime_o = prime_p;
		prime_p = prime_q;
		prime_q = next_prime(prime_q);
	}
	println!("weak primes below 1,000,000: {}", n);

	while prime_p < 10000000 {
		if prime_p < (prime_o + prime_q) / 2 {
			n += 1;
		}
		prime_o = prime_p;
		prime_p = prime_q;
		prime_q = next_prime(prime_q);
	}
	println!("weak primes below 10,000,000: {}", n);
}
First 36 strong primes: 11 17 29 37 41 59 67 71 79 97 101 107 127 137 149 163 179 191 197 223 227 239 251 269 277 281 307 311 331 347 367 379 397 419 431 439
strong primes below 1,000,000: 37723
strong primes below 10,000,000: 320991
First 36 weak primes: 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181 193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401
weak primes below 1,000,000: 37779
weak primes below 10,000,000: 321749

Scala[edit]

This example works entirely with lazily evaluated lists. It starts with a list of primes, and generates a sliding iterator that looks at each triplet of primes. Lists of strong and weak primes are built by applying the given filters then selecting the middle term from each triplet.

object StrongWeakPrimes {
  def main(args: Array[String]): Unit = {
    val bnd = 1000000
    println(
      f"""|First 36 Strong Primes: ${strongPrimes.take(36).map(n => f"$n%,d").mkString(", ")}
          |Strong Primes < 1,000,000: ${strongPrimes.takeWhile(_ < bnd).size}%,d
          |Strong Primes < 10,000,000: ${strongPrimes.takeWhile(_ < 10*bnd).size}%,d
          |
          |First 37 Weak Primes: ${weakPrimes.take(37).map(n => f"$n%,d").mkString(", ")}
          |Weak Primes < 1,000,000: ${weakPrimes.takeWhile(_ < bnd).size}%,d
          |Weak Primes < 10,000,000: ${weakPrimes.takeWhile(_ < 10*bnd).size}%,d""".stripMargin)
  }
  
  def weakPrimes: LazyList[Int] = primeTrips.filter{case a +: b +: c +: _ => b < (a + c)/2.0}.map(_(1)).to(LazyList)
  def strongPrimes: LazyList[Int] = primeTrips.filter{case a +: b +: c +: _ => b > (a + c)/2}.map(_(1)).to(LazyList)
  def primeTrips: Iterator[LazyList[Int]] = primes.sliding(3)
  def primes: LazyList[Int] = 2 #:: LazyList.from(3, 2).filter(n => !Iterator.range(3, math.sqrt(n).toInt + 1, 2).exists(n%_ == 0))
}
Output:
First 36 Strong Primes: 11, 17, 29, 37, 41, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 163, 179, 191, 197, 223, 227, 239, 251, 269, 277, 281, 307, 311, 331, 347, 367, 379, 397, 419, 431, 439
Strong Primes < 1,000,000: 37,723
Strong Primes < 10,000,000: 320,991

First 37 Weak Primes: 3, 7, 13, 19, 23, 31, 43, 47, 61, 73, 83, 89, 103, 109, 113, 131, 139, 151, 167, 181, 193, 199, 229, 233, 241, 271, 283, 293, 313, 317, 337, 349, 353, 359, 383, 389, 401
Weak Primes < 1,000,000: 37,780
Weak Primes < 10,000,000: 321,750

Sidef[edit]

Translation of: Raku
var primes = 10_000_019.primes

var (*strong, *weak, *balanced)

for k in (1 ..^ primes.end) {
    var p = primes[k]

    given((primes[k-1] + primes[k+1])/2) { |x|
        case (x > p) {     weak << p }
        case (x < p) {   strong << p }
        else         { balanced << p }
    }
}

for pr, type, d, c1, c2 in [
    [  strong, 'strong',   36, 1e6, 1e7],
    [    weak, 'weak',     37, 1e6, 1e7],
    [balanced, 'balanced', 28, 1e6, 1e7],
] {
    say ("\nFirst #{d} #{type} primes:\n", pr.first(d).map{.commify}.join(' '))
    say ("Count of #{type} primes <= #{c1.commify}:  ", pr.first_index { _ > 1e6 }.commify)
    say ("Count of #{type} primes <= #{c2.commify}: " , pr.len.commify)
}
Output:
First 36 strong primes:
11 17 29 37 41 59 67 71 79 97 101 107 127 137 149 163 179 191 197 223 227 239 251 269 277 281 307 311 331 347 367 379 397 419 431 439
Count of strong primes <= 1,000,000:  37,723
Count of strong primes <= 10,000,000: 320,991

First 37 weak primes:
3 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181 193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401
Count of weak primes <= 1,000,000:  37,780
Count of weak primes <= 10,000,000: 321,750

First 28 balanced primes:
5 53 157 173 211 257 263 373 563 593 607 653 733 947 977 1,103 1,123 1,187 1,223 1,367 1,511 1,747 1,753 1,907 2,287 2,417 2,677 2,903
Count of balanced primes <= 1,000,000:  2,994
Count of balanced primes <= 10,000,000: 21,837

Swift[edit]

import Foundation

class PrimeSieve {
    var composite: [Bool]
    
    init(size: Int) {
        composite = Array(repeating: false, count: size/2)
        var p = 3
        while p * p <= size {
            if !composite[p/2 - 1] {
                let inc = p * 2
                var q = p * p
                while q <= size {
                    composite[q/2 - 1] = true
                    q += inc
                }
            }
            p += 2
        }
    }
    
    func isPrime(number: Int) -> Bool {
        if number < 2 {
            return false
        }
        if (number & 1) == 0 {
            return number == 2
        }
        return !composite[number/2 - 1]
    }
}

func commatize(_ number: Int) -> String {
    let n = NSNumber(value: number)
    return NumberFormatter.localizedString(from: n, number: .decimal)
}

let limit1 = 1000000
let limit2 = 10000000

class PrimeInfo {
    let maxPrint: Int
    var count1: Int
    var count2: Int
    var primes: [Int]
    
    init(maxPrint: Int) {
        self.maxPrint = maxPrint
        count1 = 0
        count2 = 0
        primes = []
    }
    
    func addPrime(prime: Int) {
        count2 += 1
        if prime < limit1 {
            count1 += 1
        }
        if count2 <= maxPrint {
            primes.append(prime)
        }
    }
    
    func printInfo(name: String) {
        print("First \(maxPrint) \(name) primes: \(primes)")
        print("Number of \(name) primes below \(commatize(limit1)): \(commatize(count1))")
        print("Number of \(name) primes below \(commatize(limit2)): \(commatize(count2))")
    }
}

var strongPrimes = PrimeInfo(maxPrint: 36)
var weakPrimes = PrimeInfo(maxPrint: 37)

let sieve = PrimeSieve(size: limit2 + 100)

var p1 = 2, p2 = 3, p3 = 5
while p2 < limit2 {
    if sieve.isPrime(number: p3) {
        let diff = p1 + p3 - 2 * p2
        if diff < 0 {
            strongPrimes.addPrime(prime: p2)
        } else if diff > 0 {
            weakPrimes.addPrime(prime: p2)
        }
        p1 = p2
        p2 = p3
    }
    p3 += 2
}

strongPrimes.printInfo(name: "strong")
weakPrimes.printInfo(name: "weak")
Output:
First 36 strong primes: [11, 17, 29, 37, 41, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 163, 179, 191, 197, 223, 227, 239, 251, 269, 277, 281, 307, 311, 331, 347, 367, 379, 397, 419, 431, 439]
Number of strong primes below 1,000,000: 37,723
Number of strong primes below 10,000,000: 320,991
First 37 weak primes: [3, 7, 13, 19, 23, 31, 43, 47, 61, 73, 83, 89, 103, 109, 113, 131, 139, 151, 167, 181, 193, 199, 229, 233, 241, 271, 283, 293, 313, 317, 337, 349, 353, 359, 383, 389, 401]
Number of weak primes below 1,000,000: 37,780
Number of weak primes below 10,000,000: 321,750

Wren[edit]

Library: Wren-math
Library: Wren-fmt
import "/math" for Int
import "/fmt" for Fmt

var primes = Int.primeSieve(1e7 + 19) // next prime above 10 million
var strong = []
var weak = []
for (p in 1...primes.count-1) {
    if (primes[p] > (primes[p-1] + primes[p+1]) / 2) {
        strong.add(primes[p])
    } else if (primes[p] < (primes[p-1] + primes[p+1]) / 2) {
        weak.add(primes[p])
    }
}

System.print("The first 36 strong primes are:")
Fmt.print("$d", strong.take(36))
Fmt.print("\nThe count of the strong primes below $,d is $,d.", 1e6, strong.count{ |n| n < 1e6 })
Fmt.print("\nThe count of the strong primes below $,d is $,d.", 1e7, strong.count{ |n| n < 1e7 })

System.print("\nThe first 37 weak primes are:")
Fmt.print("$d", weak.take(37))
Fmt.print("\nThe count of the weak primes below $,d is $,d.", 1e6, weak.count{ |n| n < 1e6 })
Fmt.print("\nThe count of the weak primes below $,d is $,d.", 1e7, weak.count{ |n| n < 1e7 })
Output:
The first 36 strong primes are:
11 17 29 37 41 59 67 71 79 97 101 107 127 137 149 163 179 191 197 223 227 239 251 269 277 281 307 311 331 347 367 379 397 419 431 439

The count of the strong primes below 1,000,000 is 37,723.

The count of the strong primes below 10,000,000 is 320,991.

The first 37 weak primes are:
3 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181 193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401

The count of the weak primes below 1,000,000 is 37,780.

The count of the weak primes below 10,000,000 is 321,750.

XPL0[edit]

proc NumOut(Num);       \Output positive integer with commas
int  Num, Dig, Cnt;
[Cnt:= [0];
Num:= Num/10;
Dig:= rem(0);
Cnt(0):= Cnt(0)+1;
if Num then NumOut(Num);
Cnt(0):= Cnt(0)-1;
ChOut(0, Dig+^0);
if rem(Cnt(0)/3)=0 & Cnt(0) then ChOut(0, ^,);
];

func IsPrime(N);        \Return 'true' if odd N > 2 is prime
int  N, I;
[for I:= 3 to sqrt(N) do
    [if rem(N/I) = 0 then return false;
    I:= I+1;
    ];
return true;
];

int StrongCnt, WeakCnt, StrongCnt0, WeakCnt0, Strongs(36), Weaks(37);
int N, P0, P1, P2, T;
[StrongCnt:= 0;  WeakCnt:= 1;
Weaks(0):= 3;
N:= 7;  P1:= 3;  P2:= 5;        \handles unique case where (2+5)/2 = 3.5
repeat  if IsPrime(N) then
            [P0:= P1;  P1:= P2;  P2:= N;
            T:= (P0+P2)/2;
            if P1 > T then
                [if StrongCnt < 36 then Strongs(StrongCnt):= P1;
                StrongCnt:= StrongCnt+1;
                ];
            if P1 < T then
                [if WeakCnt < 37 then Weaks(WeakCnt):= P1;
                WeakCnt:= WeakCnt+1;
                ];
            ];
        if P1 < 1_000_000 then
            [StrongCnt0:= StrongCnt;  WeakCnt0:= WeakCnt];
        N:= N+2;
until   P1 >= 10_000_000;

Text(0, "First 36 strong primes:^M^J");
for N:= 0 to 36-1 do
    [NumOut(Strongs(N));  ChOut(0, ^ )];
Text(0, "^M^JStrong primes below 1,000,000: ");
NumOut(StrongCnt0);
Text(0, "^M^JStrong primes below 10,000,000: ");
NumOut(StrongCnt);
Text(0, "^M^JFirst 37 weak primes:^M^J");
for N:= 0 to 37-1 do
    [NumOut(Weaks(N));  ChOut(0, ^ )];
Text(0, "^M^JWeak primes below 1,000,000: ");
NumOut(WeakCnt0);
Text(0, "^M^JWeak primes below 10,000,000: ");
NumOut(WeakCnt);
CrLf(0);
]
Output:
First 36 strong primes:
11 17 29 37 41 59 67 71 79 97 101 107 127 137 149 163 179 191 197 223 227 239 251 269 277 281 307 311 331 347 367 379 397 419 431 439 
Strong primes below 1,000,000: 37,723
Strong primes below 10,000,000: 320,991
First 37 weak primes:
3 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181 193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401 
Weak primes below 1,000,000: 37,780
Weak primes below 10,000,000: 321,751

zkl[edit]

Using GMP (GNU Multiple Precision Arithmetic Library, probabilistic primes), because it is easy and fast to generate primes.

Extensible prime generator#zkl could be used instead.

var [const] BI=Import("zklBigNum");  // libGMP
const N=1e7;

pw,strong,weak := BI(1),List(),List();   // 32,0991  32,1751
ps:=(3).pump(List,'wrap{ pw.nextPrime().toInt() }).copy();  // rolling window
do{
   pp,p,pn := ps;
   if((z:=(pp.toFloat() + pn)/2)){  // 2,3,5 --> 3.5
      if(z>p)      weak  .append(p);
      else if(z<p) strong.append(p);
   }
   ps.pop(0); ps.append(pw.nextPrime().toInt());
}while(pn<=N);
foreach nm,list,psz in (T(T("strong",strong,36), T("weak",weak,37))){
   println("First %d %s primes:\n%s".fmt(psz,nm,list[0,psz].concat(" ")));
   println("Count of %s primes <= %,10d: %,8d"
	    .fmt(nm,1e6,list.reduce('wrap(s,p){ s + (p<=1e6) },0)));
   println("Count of %s primes <= %,10d: %,8d\n".fmt(nm,1e7,list.len()));
}
Output:
First 36 strong primes:
11 17 29 37 41 59 67 71 79 97 101 107 127 137 149 163 179 191 197 223 227 239 251 269 277 281 307 311 331 347 367 379 397 419 431 439
Count of strong primes <=  1,000,000:   37,723
Count of strong primes <= 10,000,000:  320,991

First 37 weak primes:
3 7 13 19 23 31 43 47 61 73 83 89 103 109 113 131 139 151 167 181 193 199 229 233 241 271 283 293 313 317 337 349 353 359 383 389 401
Count of weak primes <=  1,000,000:   37,780
Count of weak primes <= 10,000,000:  321,750