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Prime numbers whose neighboring pairs are tetraprimes: Difference between revisions

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Prime numbers whose neighboring pairs are tetraprimes (view source)

Revision as of 00:35, 29 January 2024

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Line 1:
{{draft task}}
 
;Definitions
Line 113:
IF NOT show primes THEN print( ( " " ) ) FI;
print( ( " gaps between the primes: min: ", whole( min gap, 0 ) ) );
print( ( ", average: ", whole( ROUND AVERAGE gaps[ : gap pos ], 0 ) ) );
print( ( ", median: ", whole( ROUND MEDIAN gaps[ : gap pos ], 0 ) ) );
print( ( ", max: ", whole( max gap, 0 ), newline, newline ) )
END # show neighbour paris # ;
Line 174:
 
=={{header|C}}==
{{trans|Wren}}
{{libheader|primesieve}}
{{libheader|GLib}}
<syntaxhighlight lang="c">/* gcc -O3 `pkg-config --cflags glib-2.0` tetraprime.c -o tp `pkg-config --libs glib-2.0` -lprimesieve */
This follows the lines of the Wren example except that ''primesieve'' is used to iterate through the primes rather than sieving for them in advance. As a result, runs quickly - under 0.8 seconds on my machine.
<syntaxhighlight lang="c">/* gcc `pkg-config --cflags glib-2.0` tetraprime.c -o tp `pkg-config --libs glib-2.0` -lprimesieve */
 
#include <stdio.h>
Line 188:
#define TEN_MILLION 10000000
 
size_t size;
void primeFactors(int n, int *factors, int *length) {
int* primes;
if (n < 2) return;
 
int count = 0;
void init() {
int inc[8] = {4, 2, 4, 2, 4, 6, 2, 6};
primes = (int*) primesieve_generate_primes(2, TEN_MILLION, &size, INT_PRIMES);
while (!(n%2)) {
}
factors[count++] = 2;
 
n /= 2;
bool isTetraPrime(int n) {
}
whilesize_t (!(n%3)) {i;
int p,limit, count = factors[count++]0, prevFact = 31;
for (i = 0; ni /=< 3size; ++i) {
p = primes[i];
}
limit = p*p;
while (!(n%5)) {
factors[switch (count++] = 5;){
ncase /=0: 5;
limit *= limit;
}
for (int k = 7, i = 0; k*k <= nbreak; ) {
ifcase (!(n%k))1: {
factors[count++]limit *= kp;
n /= kbreak;
}
if (limit <= n) {
while(!(n%p)) {
if (count == 4 || p == prevFact) return false;
++count;
n /= p;
prevFact = p;
}
} else {
k += inc[i]break;
i = (i + 1) % 8;
}
}
if (n > 1) {
factors[if (count++] == 4 || p == prevFact) return nfalse;
++count;
}
*lengthreturn count == count4;
}
 
boolint hasDupsprevPrime(int *pf, int lengthn) {
size_t l = 0, r = size, m;
int i;
ifwhile (lengthl ==< 1r) return false;{
for (i = 1; im <= length;(l ++i r) {/2;
if (pfprimes[im] ==> pf[i-1]n) return true;{
r = m;
} else {
l = m + 1;
}
}
return falseprimes[r-1];
}
 
bool contains(int *pf, int length, int value) {
int i;
for (i = 0; i < length; ++i) {
if (pf[i] == value) return true;
}
return false;
}
 
Line 252 ⟶ 256:
 
int main() {
size_t s;
int i, p, c, k, length, sevens, min, max, med;
int j = 100000, sevens1 = 0, sevens2 = 0;
int pf1[24], pf2[24], pf3[24], pf4[24], *gaps;
bool cond1, cond2, cond3, cond4;
const char *t;
GArray *tetras1 = g_array_new(FALSE, FALSE, sizeof(int));
GArray *tetras2 = g_array_new(FALSE, FALSE, sizeof(int));
GArray *tetras;
init();
primesieve_iterator it;
int highest5 = prevPrime(100000);
primesieve_init(&it);
int highest6 = prevPrime(1000000);
int highest7 = primes[size - 1];
setlocale(LC_NUMERIC, "");
whilefor (js <= TEN_MILLION0; s < size; ++s) {
p = primesieve_next_prime(&it)primes[s];
if (p < j) {
primeFactors(p-2, pf1, &length);
cond1 = length == 4 && !hasDups(pf1, length);
 
// process even numbers first as likely to have most factors
primeFactors(p-1, pf2, &length);
if cond2 = length == 4(isTetraPrime(p-1) && !hasDupsisTetraPrime(pf2,p-2)) length);{
g_array_append_val(tetras1, p);
if ((p-1)%7 == 0 || (p-2)%7 == 0) ++sevens1;
}
 
if primeFactors(isTetraPrime(p+1, pf3,) &length& isTetraPrime(p+2);) {
cond3 = length == 4 && !hasDupsg_array_append_val(pf3tetras2, lengthp);
if ((p+1)%7 == 0 || (p+2)%7 == 0) ++sevens2;
 
}
primeFactors(p+2, pf4, &length);
cond4 = length == 4 && !hasDups(pf4, length);
if (p == highest5 || p == highest6 || p == highest7) {
 
if (cond1 && cond2) {
g_array_append_val(tetras1, p);
if (contains(pf1, 4, 7) || contains(pf2, 4, 7)) ++sevens1;
}
 
if (cond3 && cond4) {
g_array_append_val(tetras2, p);
if (contains(pf3, 4, 7) || contains(pf4, 4, 7)) ++sevens2;
}
} else {
for (i = 0; i < 2; ++i) {
tetras = (i == 0) ? tetras1 : tetras2;
Line 294 ⟶ 290:
t = (i == 0) ? "preceding" : "following";
printf("Found %'d primes under %'d whose %s neighboring pair are tetraprimes", c, j, t);
if (jp == 100000highest5) {
printf(":\n");
for (k = 0; k < tetras->len; ++k) {
Line 317 ⟶ 313:
printf("\n");
free(gaps);
}
j *= 10;
}
Line 323 ⟶ 319:
g_array_free(tetras1, FALSE);
g_array_free(tetras2, FALSE);
primesieve_free(primes);
return 0;
}</syntaxhighlight>
Line 329 ⟶ 326:
<pre>
Identical to Wren example.
</pre>
 
 
=={{header|C#}}==
{{trans|Java}}
<syntaxhighlight lang="C#">
using System;
using System.Collections.Generic;
 
public class PrimeNumbersNeighboringPairsTetraprimes
{
private static List<int> primes;
 
public static void Main(string[] args)
{
ListPrimeNumbers(10_000_000);
 
int largestPrime5 = LargestLessThan(100_000);
int largestPrime6 = LargestLessThan(1_000_000);
int largestPrime7 = primes[primes.Count - 1];
var tetrasPreceding = new List<int>();
var tetrasFollowing = new List<int>();
int sevensPreceding = 0;
int sevensFollowing = 0;
int limit = 100_000;
 
foreach (var prime in primes)
{
if (IsTetraPrime(prime - 1) && IsTetraPrime(prime - 2))
{
tetrasPreceding.Add(prime);
if ((prime - 1) % 7 == 0 || (prime - 2) % 7 == 0)
{
sevensPreceding++;
}
}
 
if (IsTetraPrime(prime + 1) && IsTetraPrime(prime + 2))
{
tetrasFollowing.Add(prime);
if ((prime + 1) % 7 == 0 || (prime + 2) % 7 == 0)
{
sevensFollowing++;
}
}
 
if (prime == largestPrime5 || prime == largestPrime6 || prime == largestPrime7)
{
for (int i = 0; i <= 1; i++)
{
List<int> tetras = (i == 0) ? new List<int>(tetrasPreceding) : new List<int>(tetrasFollowing);
int size = tetras.Count;
int sevens = (i == 0) ? sevensPreceding : sevensFollowing;
string text = (i == 0) ? "preceding" : "following";
 
Console.Write("Found " + size + " primes under " + limit + " whose " + text + " neighboring pair are tetraprimes");
if (prime == largestPrime5)
{
Console.WriteLine(":");
for (int j = 0; j < size; j++)
{
Console.Write($"{tetras[j],7}{(j % 10 == 9 ? "\n" : "")}");
}
Console.WriteLine();
}
Console.WriteLine();
Console.WriteLine("of which " + sevens + " have a neighboring pair one of whose factors is 7.");
Console.WriteLine();
 
var gaps = new List<int>();
for (int k = 0; k < size - 1; k++)
{
gaps.Add(tetras[k + 1] - tetras[k]);
}
gaps.Sort();
int minimum = gaps[0];
int maximum = gaps[gaps.Count - 1];
int middle = Median(gaps);
Console.WriteLine("Minimum gap between those " + size + " primes: " + minimum);
Console.WriteLine("Median gap between those " + size + " primes: " + middle);
Console.WriteLine("Maximum gap between those " + size + " primes: " + maximum);
Console.WriteLine();
}
limit *= 10;
}
}
}
 
private static bool IsTetraPrime(int number)
{
int count = 0;
int previousFactor = 1;
foreach (var prime in primes)
{
int limit = prime * prime;
if (count == 0)
{
limit *= limit;
}
else if (count == 1)
{
limit *= prime;
}
if (limit <= number)
{
while (number % prime == 0)
{
if (count == 4 || prime == previousFactor)
{
return false;
}
count++;
number /= prime;
previousFactor = prime;
}
}
else
{
break;
}
}
 
if (number > 1)
{
if (count == 4 || number == previousFactor)
{
return false;
}
count++;
}
return count == 4;
}
 
private static int Median(List<int> list)
{
int size = list.Count;
if (size % 2 == 0)
{
return (list[size / 2 - 1] + list[size / 2]) / 2;
}
return list[size / 2];
}
 
private static int LargestLessThan(int number)
{
int index = primes.BinarySearch(number);
if (index > 0)
{
return primes[index - 1];
}
return primes[~index - 2];
}
 
private static void ListPrimeNumbers(int limit)
{
int halfLimit = (limit + 1) / 2;
var composite = new bool[halfLimit];
for (int i = 1, p = 3; i < halfLimit; p += 2, i++)
{
if (!composite[i])
{
for (int j = i + p; j < halfLimit; j += p)
{
composite[j] = true;
}
}
}
 
primes = new List<int> { 2 };
for (int i = 1, p = 3; i < halfLimit; p += 2, i++)
{
if (!composite[i])
{
primes.Add(p);
}
}
}
}
</syntaxhighlight>
{{out}}
<pre>
Found 49 primes under 100000 whose preceding neighboring pair are tetraprimes:
8647 15107 20407 20771 21491 23003 23531 24767 24971 27967
29147 33287 34847 36779 42187 42407 42667 43331 43991 46807
46867 51431 52691 52747 53891 54167 58567 63247 63367 69379
71711 73607 73867 74167 76507 76631 76847 80447 83591 84247
86243 87187 87803 89387 93887 97547 97847 98347 99431
 
of which 31 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 49 primes: 56
Median gap between those 49 primes: 1208
Maximum gap between those 49 primes: 6460
 
Found 46 primes under 100000 whose following neighboring pair are tetraprimes:
8293 16553 17389 18289 22153 26893 29209 33409 35509 36293
39233 39829 40493 41809 45589 48109 58393 59629 59753 59981
60493 60913 64013 64921 65713 66169 69221 71329 74093 75577
75853 77689 77933 79393 79609 82913 84533 85853 87589 87701
88681 91153 93889 96017 97381 98453
 
of which 36 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 46 primes: 112
Median gap between those 46 primes: 1460
Maximum gap between those 46 primes: 10284
 
Found 885 primes under 1000000 whose preceding neighboring pair are tetraprimes
of which 503 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 885 primes: 4
Median gap between those 885 primes: 756
Maximum gap between those 885 primes: 7712
 
Found 866 primes under 1000000 whose following neighboring pair are tetraprimes
of which 492 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 866 primes: 4
Median gap between those 866 primes: 832
Maximum gap between those 866 primes: 10284
 
Found 10815 primes under 10000000 whose preceding neighboring pair are tetraprimes
of which 5176 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 10815 primes: 4
Median gap between those 10815 primes: 648
Maximum gap between those 10815 primes: 9352
 
Found 10551 primes under 10000000 whose following neighboring pair are tetraprimes
of which 5069 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 10551 primes: 4
Median gap between those 10551 primes: 660
Maximum gap between those 10551 primes: 10284
 
 
</pre>
 
=={{header|C++}}==
<syntaxhighlight lang="c++">
#include <algorithm>
#include <cstdint>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <string>
#include <vector>
 
std::vector<uint32_t> primes;
 
void sieve_primes(const uint32_t& limit) {
std::vector<bool> marked_prime(limit + 1, true);
 
for ( uint32_t i = 2; i * i <= limit; ++i ) {
if ( marked_prime[i] ) {
for ( uint32_t j = i * i; j <= limit; j += i ) {
marked_prime[j] = false;
}
}
}
 
for ( uint32_t i = 2; i <= limit; ++i ) {
if ( marked_prime[i] ) {
primes.emplace_back(i);
}
}
}
 
uint32_t largest_less_than(const uint32_t& n) {
auto lower = std::lower_bound(primes.begin(), primes.end(), n);
return primes[std::distance(primes.begin(), lower) - 1];
}
 
uint32_t median(const std::vector<uint32_t>& list) {
if ( list.size() % 2 == 0 ) {
return ( list[list.size() / 2 - 1] + list[list.size() / 2] ) / 2;
}
return list[list.size() / 2];
}
 
bool is_tetraPrime(uint32_t n) {
uint32_t count = 0;
uint32_t previous_factor = 1;
for ( uint32_t prime : primes ) {
uint64_t limit = prime * prime;
if ( count == 0 ) {
limit *= limit;
} else if ( count == 1 ) {
limit *= prime;
}
if ( limit <= n ) {
while ( n % prime == 0 ) {
if ( count == 4 || prime == previous_factor ) {
return false;
}
count++;
n /= prime;
previous_factor = prime;
}
} else {
break;
}
}
 
if ( n > 1 ) {
if ( count == 4 || n == previous_factor ) {
return false;
}
count++;
}
return count == 4;
}
 
int main() {
sieve_primes(10'000'000);
 
const uint32_t largest_prime_5 = largest_less_than(100'000);
const uint32_t largest_prime_6 = largest_less_than(1'000'000);
const uint32_t largest_prime_7 = primes.back();
std::vector<uint32_t> tetras_preceeding;
std::vector<uint32_t> tetras_following;
uint32_t sevens_preceeding = 0;
uint32_t sevens_following = 0;
uint32_t limit = 100'000;
 
for ( const uint32_t& prime : primes ) {
if ( is_tetraPrime(prime - 1) && is_tetraPrime(prime - 2) ) {
tetras_preceeding.emplace_back(prime);
if ( ( prime - 1 ) % 7 == 0 || ( prime - 2 ) % 7 == 0 ) {
sevens_preceeding++;
}
}
 
if ( is_tetraPrime(prime + 1) && is_tetraPrime(prime + 2) ) {
tetras_following.emplace_back(prime);
if ( ( prime + 1 ) % 7 == 0 || ( prime + 2 ) % 7 == 0 ) {
sevens_following++;
}
}
 
if ( prime == largest_prime_5 || prime == largest_prime_6 || prime == largest_prime_7 ) {
for ( uint32_t i = 0; i <= 1; ++i ) {
std::vector<uint32_t> tetras = ( i == 0 ) ? tetras_preceeding : tetras_following;
const uint64_t size = tetras.size();
const uint32_t sevens = ( i == 0 ) ? sevens_preceeding : sevens_following;
const std::string text = ( i == 0 ) ? "preceding" : "following";
 
std::cout << "Found " << size << " primes under " << limit << " whose "
<< text << " neighboring pair are tetraprimes";
if ( prime == largest_prime_5 ) {
std::cout << ":" << std::endl;
for ( uint64_t j = 0; j < size; ++j ) {
std::cout << std::setw(7) << tetras[j] << ( ( j % 10 == 9 ) ? "\n" : "" );
}
std::cout << std::endl;
}
std::cout << std::endl;
std::cout << "of which " << sevens << " have a neighboring pair one of whose factors is 7."
<< std::endl << std::endl;
 
std::vector<uint32_t> gaps(size - 1, 0);
for ( uint64_t k = 0; k < size - 1; ++k ) {
gaps[k] = tetras[k + 1] - tetras[k];
}
std::sort(gaps.begin(), gaps.end());
const uint32_t minimum = gaps.front();
const uint32_t maximum = gaps.back();
const uint32_t middle = median(gaps);
std::cout << "Minimum gap between those " << size << " primes: " << minimum << std::endl;
std::cout << "Median gap between those " << size << " primes: " << middle << std::endl;
std::cout << "Maximum gap between those " << size << " primes: " << maximum << std::endl;
std::cout << std::endl;
}
limit *= 10;
}
}
}
</syntaxhighlight>
{{ out }}
<pre>
Found 49 primes under 100000 whose preceding neighboring pair are tetraprimes:
8647 15107 20407 20771 21491 23003 23531 24767 24971 27967
29147 33287 34847 36779 42187 42407 42667 43331 43991 46807
46867 51431 52691 52747 53891 54167 58567 63247 63367 69379
71711 73607 73867 74167 76507 76631 76847 80447 83591 84247
86243 87187 87803 89387 93887 97547 97847 98347 99431
 
of which 31 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 49 primes: 56
Median gap between those 49 primes: 1208
Maximum gap between those 49 primes: 6460
 
Found 46 primes under 100000 whose following neighboring pair are tetraprimes:
8293 16553 17389 18289 22153 26893 29209 33409 35509 36293
39233 39829 40493 41809 45589 48109 58393 59629 59753 59981
60493 60913 64013 64921 65713 66169 69221 71329 74093 75577
75853 77689 77933 79393 79609 82913 84533 85853 87589 87701
88681 91153 93889 96017 97381 98453
 
of which 36 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 46 primes: 112
Median gap between those 46 primes: 1460
Maximum gap between those 46 primes: 10284
 
Found 885 primes under 1000000 whose preceding neighboring pair are tetraprimes
of which 503 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 885 primes: 4
Median gap between those 885 primes: 756
Maximum gap between those 885 primes: 7712
 
Found 866 primes under 1000000 whose following neighboring pair are tetraprimes
of which 492 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 866 primes: 4
Median gap between those 866 primes: 832
Maximum gap between those 866 primes: 10284
 
Found 10815 primes under 10000000 whose preceding neighboring pair are tetraprimes
of which 5176 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 10815 primes: 4
Median gap between those 10815 primes: 648
Maximum gap between those 10815 primes: 9352
 
Found 10551 primes under 10000000 whose following neighboring pair are tetraprimes
of which 5069 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 10551 primes: 4
Median gap between those 10551 primes: 660
Maximum gap between those 10551 primes: 10284
</pre>
 
Line 466 ⟶ 896:
)
 
const LIMIT = int(1e7)
func hasDups(pf []int) bool {
var primes = rcu.Primes(LIMIT)
le := len(pf)
 
if le == 1 {
func isTetraPrime(n int) bool {
return false
}count := 0;
for iprevFact := 1; i < le; i++ {
for _, p := if pf[i] ==range pf[i-1]primes {
limit := p * return truep
if count == 0 {
limit *= limit
} else if count == 1 {
limit *= p
}
if limit <= n {
for n % p == 0 {
if count == 4 || p == prevFact {
return false
}
count++
n /= p
prevFact = p
}
} else {
break
}
}
returnif falsen > 1 {
if count == 4 || n == prevFact {
}
return false
 
func contains(pf []int, value int) bool {
for i := 0; i < len(pf); i++ {
if pf[i] == value {
return true
}
count++
}
return falsecount == 4
}
}
 
// Note that 'gaps' will only contain even numbers here.
func median(gaps []int) int {
Line 499 ⟶ 942:
 
func main() {
const LIMIT = int(1e7)
primes := rcu.Primes(LIMIT)
highest5 := primes[sort.SearchInts(primes, int(1e5))-1]
highest6 := primes[sort.SearchInts(primes, int(1e6))-1]
Line 508 ⟶ 949:
j := 100_000
for _, p := range primes {
// process even numbers first as likely to have most factors
pf1 := rcu.PrimeFactors(p - 2)
cond1if := lenisTetraPrime(pf1p-1) == 4 && !hasDupsisTetraPrime(pf1p-2) {
 
pf2 := rcu.PrimeFactors(p - 1)
cond2 := len(pf2) == 4 && !hasDups(pf2)
 
pf3 := rcu.PrimeFactors(p + 1)
cond3 := len(pf3) == 4 && !hasDups(pf3)
 
pf4 := rcu.PrimeFactors(p + 2)
cond4 := len(pf4) == 4 && !hasDups(pf4)
 
if cond1 && cond2 {
tetras1 = append(tetras1, p)
if contains(pf1, 7p-1)%7 == 0 || contains(pf2, 7p-2)%7 == 0 {
sevens1++
}
}
 
if cond3 && cond4 {
if isTetraPrime(p+1) && isTetraPrime(p+2) {
tetras2 = append(tetras2, p)
if contains(pf3, 7p+1)%7 == 0 || contains(pf4, 7p+2)%7 == 0 {
sevens2++
}
}
 
if p == highest5 || p == highest6 || p == highest7 {
for i := 0; i < 2; i++ {
Line 584 ⟶ 1,016:
</pre>
 
=={{header|J}}==
 
For this task we could use a couple tools -- one to enumerate primes less than some limit, and one to determine if a number is a tetraprime:
<syntaxhighlight lang=J>primeslt=: i.&.(p:inv)
 
tetrap=: 0:`(4=#@~.)@.(4=#)@q: ::0:"0</syntaxhighlight>
 
Thus:
 
<syntaxhighlight lang=J> NB. (1) primes less than 1e5 preceeded by two tetraprimes
{{y#~*/tetrap 1 2-~/y}} primeslt 1e5
8647 15107 20407 20771 21491 23003 23531 24767 24971 27967 29147 33287 34847 36779 42187 42407 42667 43331 43991 46807 46867 51431 52691 52747 53891 54167 58567 63247 63367 69379 71711 73607 73867 74167 76507 76631 76847 80447 83591 84247 86243 87187 87803...
NB. (2) primes less than 1e5 followed by two tetraprimes
{{y#~*/tetrap 1 2+/y}} primeslt 1e5
8293 16553 17389 18289 22153 26893 29209 33409 35509 36293 39233 39829 40493 41809 45589 48109 58393 59629 59753 59981 60493 60913 64013 64921 65713 66169 69221 71329 74093 75577 75853 77689 77933 79393 79609 82913 84533 85853 87589 87701 88681 91153 93889...
NB. (3a) how many primes from (1) have 7 in a factor of a number in the preceeding pair?
+/0+./ .=7|1 2-~/{{y#~*/tetrap 1 2-~/y}} primeslt 1e5
31
NB. (3b) how many primes from (2) have 7 in a factor of a number in the following pair?
+/0+./ .=7|1 2+/{{y#~*/tetrap 1 2+/y}} primeslt 1e5
36
NB. (4a) minimum, maximum gap between primes in (1)
(<./,>./)2 -~/\{{y#~*/tetrap 1 2-~/y}} primeslt 1e5
56 6460
NB. (4b) minimum, maximum gap between primes in (2)
(<./,>./)2 -~/\{{y#~*/tetrap 1 2+/y}} primeslt 1e5
112 10284
NB. number of type (1) primes but for primes less than 1e6
#{{y#~*/tetrap 1 2-~/y}} primeslt 1e6
885
NB. number of type (2) primes but for primes less than 1e6
#{{y#~*/tetrap 1 2+/y}} primeslt 1e5
46
NB. count of type (3a) for primes less than 1e6
+/0+./ .=7|1 2-~/{{y#~*/tetrap 1 2-~/y}} primeslt 1e6
503
NB. count of type (3b) for primes less than 1e6
+/0+./ .=7|1 2+/{{y#~*/tetrap 1 2+/y}} primeslt 1e6
492
NB. gaps of type (4a) for primes less than 1e6
(<./,>./)2 -~/\{{y#~*/tetrap 1 2-~/y}} primeslt 1e6
4 7712
NB. gaps of type (4b) for primes less than 1e6
(<./,>./)2 -~/\{{y#~*/tetrap 1 2+/y}} primeslt 1e6
4 10284</syntaxhighlight>
 
=={{header|Java}}==
<syntaxhighlight lang="java">
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
 
public final class PrimeNumbersNeighboringPairsTetraprimes {
 
public static void main(String[] aArgs) {
listPrimeNumbers(10_000_000);
 
final int largest_prime_5 = largestLessThan(100_000);
final int largest_prime_6 = largestLessThan(1_000_000);
final int largest_prime_7 = primes.get(primes.size() - 1);
List<Integer> tetras_preceeding = new ArrayList<Integer>();
List<Integer> tetras_following = new ArrayList<Integer>();
int sevens_preceeding = 0;
int sevens_following = 0;
int limit = 100_000;
 
for ( int prime : primes ) {
if ( isTetraPrime(prime - 1) && isTetraPrime(prime - 2) ) {
tetras_preceeding.add(prime);
if ( ( prime - 1 ) % 7 == 0 || ( prime - 2 ) % 7 == 0 ) {
sevens_preceeding += 1;
}
}
 
if ( isTetraPrime(prime + 1) && isTetraPrime(prime + 2) ) {
tetras_following.add(prime);
if ( ( prime + 1 ) % 7 == 0 || ( prime + 2 ) % 7 == 0 ) {
sevens_following += 1;
}
}
 
if ( prime == largest_prime_5 || prime == largest_prime_6 || prime == largest_prime_7 ) {
for ( int i = 0; i <= 1; i++ ) {
List<Integer> tetras = ( i == 0 ) ?
new ArrayList<Integer>(tetras_preceeding) : new ArrayList<Integer>(tetras_following);
final int size = tetras.size();
final int sevens = ( i == 0 ) ? sevens_preceeding : sevens_following;
final String text = ( i == 0 ) ? "preceding" : "following";
 
System.out.print("Found " + size + " primes under " + limit + " whose "
+ text + " neighboring pair are tetraprimes");
if ( prime == largest_prime_5 ) {
System.out.println(":");
for ( int j = 0; j < size; j++ ) {
System.out.print(String.format("%7d%s", tetras.get(j), ( j % 10 == 9 ) ? "\n" : "" ));
}
System.out.println();
}
System.out.println();
System.out.println("of which " + sevens + " have a neighboring pair one of whose factors is 7.");
System.out.println();
 
List<Integer> gaps = new ArrayList<Integer>(size - 1);
for ( int k = 0; k < size - 1; k++ ) {
gaps.add(tetras.get(k + 1) - tetras.get(k));
}
Collections.sort(gaps);
final int minimum = gaps.get(0);
final int maximum = gaps.get(gaps.size() - 1);
final int middle = median(gaps);
System.out.println("Minimum gap between those " + size + " primes: " + minimum);
System.out.println("Median gap between those " + size + " primes: " + middle);
System.out.println("Maximum gap between those " + size + " primes: " + maximum);
System.out.println();
}
limit *= 10;
}
}
}
private static boolean isTetraPrime(int aNumber) {
int count = 0;
int previousFactor = 1;
for ( int prime : primes ) {
int limit = prime * prime;
if ( count == 0 ) {
limit *= limit;
} else if ( count == 1 ) {
limit *= prime;
}
if ( limit <= aNumber ) {
while ( aNumber % prime == 0 ) {
if ( count == 4 || prime == previousFactor ) {
return false;
}
count += 1;
aNumber /= prime;
previousFactor = prime;
}
} else {
break;
}
}
 
if ( aNumber > 1 ) {
if ( count == 4 || aNumber == previousFactor ) {
return false;
}
count += 1;
}
return count == 4;
}
private static int median(List<Integer> aList) {
if ( aList.size() % 2 == 0 ) {
return ( aList.get(aList.size() / 2 - 1) + aList.get(aList.size() / 2) ) / 2;
}
return aList.get(aList.size() / 2);
}
private static int largestLessThan(int aNumber) {
final int index = Collections.binarySearch(primes, aNumber);
if ( index > 0 ) {
return primes.get(index - 1);
}
return primes.get(-index - 2);
}
private static void listPrimeNumbers(int aLimit) {
final int halfLimit = ( aLimit + 1 ) / 2;
boolean[] composite = new boolean[halfLimit];
for ( int i = 1, p = 3; i < halfLimit; p += 2, i++ ) {
if ( ! composite[i] ) {
for ( int j = i + p; j < halfLimit; j += p ) {
composite[j] = true;
}
}
}
primes = new ArrayList<Integer>();
primes.add(2);
for ( int i = 1, p = 3; i < halfLimit; p += 2, i++ ) {
if ( ! composite[i] ) {
primes.add(p);
}
}
}
private static List<Integer> primes;
 
}
</syntaxhighlight>
{{ out }}
<pre>
Found 49 primes under 100000 whose preceding neighboring pair are tetraprimes:
8647 15107 20407 20771 21491 23003 23531 24767 24971 27967
29147 33287 34847 36779 42187 42407 42667 43331 43991 46807
46867 51431 52691 52747 53891 54167 58567 63247 63367 69379
71711 73607 73867 74167 76507 76631 76847 80447 83591 84247
86243 87187 87803 89387 93887 97547 97847 98347 99431
 
of which 31 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 49 primes: 56
Median gap between those 49 primes: 1208
Maximum gap between those 49 primes: 6460
 
Found 46 primes under 100000 whose following neighboring pair are tetraprimes:
8293 16553 17389 18289 22153 26893 29209 33409 35509 36293
39233 39829 40493 41809 45589 48109 58393 59629 59753 59981
60493 60913 64013 64921 65713 66169 69221 71329 74093 75577
75853 77689 77933 79393 79609 82913 84533 85853 87589 87701
88681 91153 93889 96017 97381 98453
 
of which 36 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 46 primes: 112
Median gap between those 46 primes: 1460
Maximum gap between those 46 primes: 10284
 
Found 885 primes under 1000000 whose preceding neighboring pair are tetraprimes
of which 503 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 885 primes: 4
Median gap between those 885 primes: 756
Maximum gap between those 885 primes: 7712
 
Found 866 primes under 1000000 whose following neighboring pair are tetraprimes
of which 492 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 866 primes: 4
Median gap between those 866 primes: 832
Maximum gap between those 866 primes: 10284
 
Found 10815 primes under 10000000 whose preceding neighboring pair are tetraprimes
of which 5176 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 10815 primes: 4
Median gap between those 10815 primes: 648
Maximum gap between those 10815 primes: 9352
 
Found 10551 primes under 10000000 whose following neighboring pair are tetraprimes
of which 5069 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 10551 primes: 4
Median gap between those 10551 primes: 660
Maximum gap between those 10551 primes: 10284
</pre>
 
=={{header|Julia}}==
Line 598 ⟶ 1,278:
let
primes1M = primes(10^7)
pre1M = filter(are_preceding_tetraprimes, primes1M)
fol1M = filter(are_following_tetraprimes, primes1M)
pre100k = filter(<(100_000), pre1M)
Line 614 ⟶ 1,293:
f_gaps100k = [fol1M[i] - fol1M[i - 1] for i in 2:lastindex(fol1M) if fol1M[i] < 100_000]
 
pmin100k, pmedian100k, pmax100k = minimum(p_gaps100k), median(p_gaps100k), maximum(p_gaps100k)
fmin100k, fmedian100k, fmax100k = minimum(f_gaps100k), median(f_gaps100k), maximum(f_gaps100k)
pmin1M, pmedian1M, pmax1M = minimum(p_gaps1M), median(p_gaps1M), maximum(p_gaps1M)
fmin1M, fmedian1M, fmax1M = minimum(f_gaps1M), median(f_gaps1M), maximum(f_gaps1M)
pmin100k, pmedian100k, pmax100k = minimum(p_gaps100k), median(p_gaps100k), maximum(p_gaps100k)
fmin100k, fmedian100k, fmax100k = minimum(f_gaps100k), median(f_gaps100k), maximum(f_gaps100k)
 
for (tet, s, s2, tmin, tmed, tmax, t7) in [
(pre100k, "100,000", "preceding", pmin100k, pmedian100k, pmax100k, pre100k_with7),
(fol100k, "100,000", "following", fmin100k, fmedian100k, fmax100k, fol100k_with7),
(pre1M, "1,000,000", "preceding", pmin1M, pmedian1M, pmax1M, pre1M_with7),
(fol1M, "1,000,000", "following", fmin1M, fmedian1M, fmax1M, fol1M_with7),
]
print("Found $(length(tet)) primes under $s whose preceding$s2 neighboring pair are tetraprimes")
if s == "100,000"
println(":")
Line 648 ⟶ 1,327:
Of those primes, 31 have a neighboring pair one of whose factors is 7.
 
Found 46 primes under 100,000 whose precedingfollowing neighboring pair are tetraprimes:
8293 16553 17389 18289 22153 26893 29209 33409 35509 36293
39233 39829 40493 41809 45589 48109 58393 59629 59753 59981
Line 661 ⟶ 1,340:
Of those primes, 5176 have a neighboring pair one of whose factors is 7.
 
Found 10551 primes under 1,000,000 whose precedingfollowing neighboring pair are tetraprimes.
Minimum, median, and maximum gaps between those primes: 4 660.0 10284
Of those primes, 5069 have a neighboring pair one of whose factors is 7.
</pre>
 
=={{header|Nim}}==
To improve performance, we used <code>int32</code> instead of <code>int</code> which are 64 bits long on 64 bits platforms. We also avoided to search all the factors by stopping if the number of factors is greater than four or if the same factor occurs more than one time.
<syntaxhighlight lang="Nim">import std/[algorithm, bitops, math, strformat, strutils, sugar]
 
### Sieve of Erathostenes.
 
type Sieve = object
data: seq[byte]
 
func `[]`(sieve: Sieve; idx: Positive): bool =
## Return value of element at index "idx".
let idx = idx shr 1
let iByte = idx shr 3
let iBit = idx and 7
result = sieve.data[iByte].testBit(iBit)
 
func `[]=`(sieve: var Sieve; idx: Positive; val: bool) =
## Set value of element at index "idx".
let idx = idx shr 1
let iByte = idx shr 3
let iBit = idx and 7
if val: sieve.data[iByte].setBit(iBit)
else: sieve.data[iByte].clearBit(iBit)
 
func newSieve(lim: Positive): Sieve =
## Create a sieve with given maximal index.
result.data = newSeq[byte]((lim + 16) shr 4)
 
func initPrimes(lim: int32): seq[int32] =
## Initialize the list of primes from 3 to "lim".
var composite = newSieve(lim)
composite[1] = true
for n in countup(3, sqrt(lim.toFloat).int, 2):
if not composite[n]:
for k in countup(n * n, lim, 2 * n):
composite[k] = true
for n in countup(3i32, lim, 2):
if not composite[n]:
result.add n
 
 
### Task functions.
 
func isTetraPrime(n: int32): bool =
## Return true if "n" is a tetraprime.
var n = n
if n < 2: return
const Inc = [4, 2, 4, 2, 4, 6, 2, 6] # Wheel.
var count = 0
 
if (n and 1) == 0:
inc count
n = n shr 1
if (n and 1) == 0: return
if n mod 3 == 0:
inc count
n = n div 3
if n mod 3 == 0: return
if n mod 5 == 0:
inc count
n = n div 5
if n mod 5 == 0: return
var k = 7i32
var i = 0
while k * k <= n:
if n mod k == 0:
inc count
n = n div k
if count > 4 or n mod k == 0: return
inc k, Inc[i]
i = (i + 1) and 7
if n > 1: inc count
result = count == 4
 
func median(a: openArray[int32]): int32 =
## Return the median value of "a".
let m = a.len div 2
result = if (a.len and 1) == 0: (a[m] + a[m-1]) div 2 else: a[m]
 
 
type Position {.pure.} = enum Preceding = "preceding", Following = "following"
 
proc printResult(list: seq[int32]; count: int; lim: int; pos: Position; display: bool) =
## Print the result for the given list and the given count.
let c = if display: ':' else: '.'
let lim = insertSep($lim)
echo &"Found {list.len} primes under {lim} whose {pos} neighboring pair are tetraprimes{c}"
if display:
for i, p in list:
stdout.write &"{p:5}"
stdout.write if i mod 10 == 9 or i == list.high: '\n' else: ' '
echo()
echo &" Of which {count} have a neighboring pair one of whose factors is 7.\n"
var gaps = collect(for i in 1..list.high: list[i] - list[i - 1])
gaps.sort()
echo &" Minimum gap between those {list.len} primes: {gaps[0]}"
echo &" Median gap between those {list.len} primes: {gaps.median}"
echo &" Maximum gap between those {list.len} primes: {gaps[^1]}"
echo()
 
 
const Steps = [int32 100_000, 1_000_000, 10_000_000]
 
var list1: seq[int32] # Prime whose preceding neighboring pair are tetraprimes.
var list2: seq[int32] # Prime whose following neighboring pair are tetraprimes.
var count1 = 0 # Number of primes from "list1" with one value of the pairs multiple of 7.
var count2 = 0 # Number of primes from "list2" with one value of the pairs multiple of 7.
 
let primes = initPrimes(Steps[^1])
 
var limit = Steps[0]
var iLimit = 0
var display = true # True to display the primes.
var last = primes[^1]
 
for p in primes:
 
if p >= limit or p == last:
printResult(list1, count1, limit, Preceding, display)
printResult(list2, count2, limit, Following, display)
if iLimit == Steps.high: break
inc iLimit
limit = Steps[iLimit]
display = false # Don't display next primes.
 
if isTetraPrime(p - 2) and isTetraPrime(p - 1):
list1.add p
if (p - 2) mod 7 in [0, 6]:
inc count1
 
if isTetraPrime(p + 1) and isTetraPrime(p + 2):
list2.add p
if (p + 1) mod 7 in [0, 6]:
inc count2
</syntaxhighlight>
 
{{out}}
<pre>Found 49 primes under 100_000 whose preceding neighboring pair are tetraprimes:
8647 15107 20407 20771 21491 23003 23531 24767 24971 27967
29147 33287 34847 36779 42187 42407 42667 43331 43991 46807
46867 51431 52691 52747 53891 54167 58567 63247 63367 69379
71711 73607 73867 74167 76507 76631 76847 80447 83591 84247
86243 87187 87803 89387 93887 97547 97847 98347 99431
 
Of which 31 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 49 primes: 56
Median gap between those 49 primes: 1208
Maximum gap between those 49 primes: 6460
 
Found 46 primes under 100_000 whose following neighboring pair are tetraprimes:
8293 16553 17389 18289 22153 26893 29209 33409 35509 36293
39233 39829 40493 41809 45589 48109 58393 59629 59753 59981
60493 60913 64013 64921 65713 66169 69221 71329 74093 75577
75853 77689 77933 79393 79609 82913 84533 85853 87589 87701
88681 91153 93889 96017 97381 98453
 
Of which 36 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 46 primes: 112
Median gap between those 46 primes: 1460
Maximum gap between those 46 primes: 10284
 
Found 885 primes under 1_000_000 whose preceding neighboring pair are tetraprimes.
Of which 503 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 885 primes: 4
Median gap between those 885 primes: 756
Maximum gap between those 885 primes: 7712
 
Found 866 primes under 1_000_000 whose following neighboring pair are tetraprimes.
Of which 492 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 866 primes: 4
Median gap between those 866 primes: 832
Maximum gap between those 866 primes: 10284
 
Found 10815 primes under 10_000_000 whose preceding neighboring pair are tetraprimes.
Of which 5176 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 10815 primes: 4
Median gap between those 10815 primes: 648
Maximum gap between those 10815 primes: 9352
 
Found 10551 primes under 10_000_000 whose following neighboring pair are tetraprimes.
Of which 5069 have a neighboring pair one of whose factors is 7.
 
Minimum gap between those 10551 primes: 4
Median gap between those 10551 primes: 660
Maximum gap between those 10551 primes: 10284</pre>
 
=={{header|Pascal}}==
==={{header|Free Pascal}}===
uses [[Extensible_prime_generator#Pascal|Extensible_prime_generator]]<br>
Generating and bitmarking all tetraprimes up to limit.So no time consuming check has to be done.
<syntaxhighlight lang="pascal">
program TetraPrimes;
{$IFDEF FPC}{$MODE DELPHI}{$OPTIMIZATION ON,ALL}
{$CodeAlign proc=1,loop=1} // for Ryzen 5xxx
{$ENDIF}
{$IFDEF Windows}{$APPTYPE CONSOLE}{$ENDIF}
uses
sysutils,primsieve;
const
cLimit =1000*1000*1000;
 
MinTriple = 2*3*5;
MInQuad = MinTriple*7;
cBits2pow = 6; // 2^ 6 = 64-Bit
cMask = 1 shl cBits2pow-1;
 
type
tIdx = 0..1 shl cBits2pow-1;
tSetBits = set of tIdx;
tMyResult = record
mr_Limit,
mr_cnt,
mr_cnt7,
mr_min,
mr_median,
mr_gapsum,
mr_max : Uint32;
mr_dir : boolean;
end;
var
MarkTetraPrimes : array of tSetBits;
MyPrimes : array of Uint32;
GapCnt: array[0..14660 shr 2] of Uint32;
SmallTetraPrimes : array[0..49] of Uint32;
MyResult : tMyResult;
MaxPrime,HighMyPrimes,count : Uint32;
procedure GenerateTetraPrimes(Factor:NativeUint;MinIdx,CountOfFactors:Uint32);
var
fp,
p : NativeUint;
begin
dec(CountOfFactors);
If (CountOfFactors = 0) then
begin
For MinIdx := MinIdx to HighMyPrimes do
begin
fp := Factor * MyPrimes[MinIdx];
if fp > cLimit then
BREAK;
inc(count);
include(MarkTetraPrimes[fp SHR cBits2pow],fp AND cMask);
end;
end
else
For MinIdx := MinIdx to HighMyPrimes-CountOfFactors do
begin
p := MyPrimes[MinIdx];
fp :=p*Factor;
case CountOfFactors of
2 : p *= p;
3 : p *= p*p;
else
end;
if fp*p < cLimit then
GenerateTetraPrimes(fp,MinIdx+1,CountOfFactors);
end;
end;
procedure GetTetraPrimes(Limit:Uint32);
var
l,
p,i : Uint32;
Begin
setlength(MarkTetraPrimes, Limit shr cBits2pow);
//estimate count of primes
if limit < 10 then
setlength(MyPrimes,4)
else
setlength(MyPrimes,round(Limit/(ln(limit)-1.5)));
 
InitPrime;
L :=Limit DIV MinTriple;
i := 0;
repeat
p := NextPrime;
MyPrimes[i] := p;
inc(i);
until p > l;
HighMyPrimes := i;
repeat
p := NextPrime;
MyPrimes[i] := p;
inc(i);
until p > limit;
setlength(MyPrimes,i-1);
MaxPrime := MyPrimes[HighMyPrimes];
GenerateTetraPrimes(1,0,4);
end;
 
function TwoInRow(p : NativeUint;dirUp:Boolean = false):boolean;
var
delta : NativeUint;
begin
if (p < minquad) then
EXIT(false);
delta := ORD(DirUp)*2-1;//= +1,-1
if 2*delta+p >cLimit then
EXIT(false);
p += delta;
if (p AND cMask) in MarkTetraPrimes[p SHR cBits2pow] then
begin
p += delta;
if (p AND cMask) in MarkTetraPrimes[p SHR cBits2pow] then
EXIT(true);
end;
EXIT(false);
end;
 
procedure CheckLimitDirUp(var Res:tMyResult;Limit:NativeUint;dirUp:boolean);
var
p,Last,GapSum,cnt,cnt7 : UInt32;
i,d : Int32;
Begin
FillChar(GapCnt,SizeOf(GapCnt),#0);
Last := 0;
cnt := 0;
cnt7 := 0;
GapSum := 0;
if dirUp then
d := 1
else
d := -1;
for i := 0 to High(myPrimes) do
begin
p := MyPrimes[i];
If p > Limit then
BREAK;
if TwoInRow(p,dirUp) then
Begin
If Last <> 0 then
Begin
Last := (p-Last) shr 2;
GapSum+=Last;
Inc(GapCnt[Last]);
end;
Last := p;
if limit <= 100*1000 then
SmallTetraPrimes[cnt] := p;
 
inc(cnt);
p += d;
if p MOD 7 = 0 then
inc(cnt7)
else
if (p+d) MOD 7 = 0 then
inc(cnt7);
end;
end;
with res do
begin
mr_limit:= Limit;
mr_cnt := cnt;
mr_cnt7 := cnt7;
mr_dir := dirUp;
end;
If cnt > 1 then
Begin
For i := 0 to High(GapCnt) do
IF GapCnt[i] <> 0 then
begin
res.mr_min := i shl 2;
BREAK;
end;
For i := High(GapCnt) downto 0 do
IF GapCnt[i] <> 0 then
begin
res.mr_max := i shl 2;
BREAK;
end;
//median;
Limit := cnt DIV 2;
p := 0;
For i := 0 to res.mr_max do
Begin
inc(p,GapCnt[i]);
IF p >= Limit then
begin
res.mr_median := i*4;
BREAK;
end;
end;
res.mr_GapSum := GapSum*4;
end;
if limit <= 100*1000 then
writeln;
end;
 
procedure Out_Res(const res:tMyResult);
const
Direction : array[Boolean]of string =(' preceded ',' followed ');
var
i : integer;
begin
with res do
Begin
writeln('Primes below ',mr_limit,Direction[mr_dir],' by a tetraprime pair:');
if mr_cnt < 50 then
begin
For i := 0 to mr_cnt-1 do
Begin
write(SmallTetraPrimes[i]:7);
if (i+1) MOD 10 = 0 then
writeln;
end;
writeln;
end;
writeln(#9,'Found ',mr_cnt,' such primes of which ',mr_cnt7,' have 7 as a factor of one of the pair');
writeln(#9#9'GapCnt between the primes: min: ',mr_min,
', average: ',mr_GapSum/(mr_cnt-1):0:1,
', median: ',mr_median,
', max: ',mr_max);
end;
end;
 
procedure CheckLimit(Limit:NativeUint);
const
preceded = false;
followed = true;
 
var
myResult :TMyResult;
begin
CheckLimitDirUp(myResult,Limit,preceded);
Out_Res(myResult);
CheckLimitDirUp(myResult,Limit,followed);
Out_Res(myResult);
writeln;
end;
 
var
i : Uint32;
Begin
GetTetraPrimes(cLimit);
GenerateTetraPrimes(1,0,4);
i := 100000;
repeat
CheckLimit(i);
i *= 10
until i >= cLimit;
CheckLimit(cLimit);
end.
</syntaxhighlight>
{{out|@home ( 5600G @ 4.4 Ghz )}}
<pre>Primes below 100000 preceded by a tetraprime pair:
8647 15107 20407 20771 21491 23003 23531 24767 24971 27967
29147 33287 34847 36779 42187 42407 42667 43331 43991 46807
46867 51431 52691 52747 53891 54167 58567 63247 63367 69379
71711 73607 73867 74167 76507 76631 76847 80447 83591 84247
86243 87187 87803 89387 93887 97547 97847 98347 99431
Found 49 such primes of which 31 have 7 as a factor of one of the pair
GapCnt between the primes: min: 56, average: 1891.3, median: 1180, max: 6460
 
Primes below 100000 followed by a tetraprime pair:
8293 16553 17389 18289 22153 26893 29209 33409 35509 36293
39233 39829 40493 41809 45589 48109 58393 59629 59753 59981
60493 60913 64013 64921 65713 66169 69221 71329 74093 75577
75853 77689 77933 79393 79609 82913 84533 85853 87589 87701
88681 91153 93889 96017 97381 98453
Found 46 such primes of which 36 have 7 as a factor of one of the pair
GapCnt between the primes: min: 112, average: 2003.6, median: 1460, max: 10284
 
 
Primes below 1000000 preceded by a tetraprime pair:
Found 885 such primes of which 503 have 7 as a factor of one of the pair
GapCnt between the primes: min: 4, average: 1119.5, median: 756, max: 7712
 
Primes below 1000000 followed by a tetraprime pair:
Found 866 such primes of which 492 have 7 as a factor of one of the pair
GapCnt between the primes: min: 4, average: 1146.0, median: 832, max: 10284
 
 
Primes below 10000000 preceded by a tetraprime pair:
Found 10815 such primes of which 5176 have 7 as a factor of one of the pair
GapCnt between the primes: min: 4, average: 923.9, median: 648, max: 9352
 
Primes below 10000000 followed by a tetraprime pair:
Found 10551 such primes of which 5069 have 7 as a factor of one of the pair
GapCnt between the primes: min: 4, average: 947.0, median: 660, max: 10284
//real 0m0,033s
 
Primes below 100000000 preceded by a tetraprime pair:
Found 110865 such primes of which 47197 have 7 as a factor of one of the pair
GapCnt between the primes: min: 4, average: 901.9, median: 632, max: 11892
 
Primes below 100000000 followed by a tetraprime pair:
Found 110192 such primes of which 47308 have 7 as a factor of one of the pair
GapCnt between the primes: min: 4, average: 907.4, median: 640, max: 11000
//real 0m0,458s
 
Primes below 1000000000 preceded by a tetraprime pair:
Found 1081567 such primes of which 423195 have 7 as a factor of one of the pair
GapCnt between the primes: min: 4, average: 924.6, median: 648, max: 14660
Primes below 1000000000 followed by a tetraprime pair:
Found 1081501 such primes of which 423572 have 7 as a factor of one of the pair
GapCnt between the primes: min: 4, average: 924.6, median: 648, max: 12100
 
real 0m10,578s</pre>
 
=={{header|Phix}}==
{{trans|Wren}}
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">constant</span> <span style="color: #000000;">primes</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">get_primes_le</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1e7</span><span style="color: #0000FF;">)</span>
Line 711 ⟶ 1,896:
{{out}}
Same as Wren
 
=={{header|Raku}}==
{{trans|Wren}}
<syntaxhighlight lang="raku" line># 20230721 Raku programming solution
 
my @primes = (2..1e7).grep: *.is-prime; # cannot do lazy here
 
sub median { # based on https://rosettacode.org/wiki/Averages/Median#Raku
return { ( .[(*-1) div 2] + .[* div 2] ) / 2 }(@_) # for already sorted
}
 
sub isTetraPrime ($n is copy) { # is cached {
my ($count,$prevFact) = 0, 1;
for @primes -> \p {
my $limit = p * p;
if $count == 0 {
$limit = $limit * $limit
} elsif $count == 1 {
$limit *= p
}
if $limit <= $n {
while $n %% p {
return False if ( $count == 4 or p == $prevFact );
$count++;
$n div= p;
$prevFact = p
}
} else {
last
}
}
if $n > 1 {
return False if ( $count == 4 or $n == $prevFact );
$count++
}
return $count == 4
}
 
my ( $j, @tetras1, @tetras2, $sevens1, $sevens2 ) = 1e5;
 
my \highest7 = @primes.[*-1];
my \highest6 = @primes.first: * < 1e6, :end;
my \highest5 = @primes.first: * < 1e5, :end;
 
for @primes -> \p {
if isTetraPrime p-1 and isTetraPrime p-2 {
@tetras1.push: p;
$sevens1++ if ( (p-1) %% 7 or (p-2) %% 7 );
}
if isTetraPrime p+1 and isTetraPrime p+2 {
@tetras2.push: p;
$sevens2++ if ( (p+1) %% 7 or (p+2) %% 7 );
}
if p == highest5 | highest6 | highest7 {
for 0,1 -> \i {
my (\sevens, \t, @tetras) := i == 0
?? ( $sevens1, "preceding", @tetras1 )
!! ( $sevens2, "following", @tetras2 );
my \c = @tetras.elems;
 
say "Found {c} primes under $j whose {t} neighboring pair are tetraprimes:";
if p == highest5 {
say [~] $_>>.fmt('%6s') for @tetras.rotor(10,:partial);
}
say "of which {sevens} have a neighboring pair one of whose factors is 7.\n";
my \gaps = ( @tetras.rotor(2=>-1).map: { .[1] - .[0] } ).sort;
my (\Min,\Max,\Med) = gaps[0], gaps[*-1], median(gaps);
say "Minimum gap between those {c} primes : {Min}";
say "Median gap between those {c} primes : {Med}";
say "Maximum gap between those {c} primes : {Max}";
say()
}
$j *= 10
}
}</syntaxhighlight>
{{out}} Same as Wren
 
=={{header|Wren}}==
{{libheader|Wren-math}}
{{libheader|Wren-sort}}
{{libheader|Wren-seq}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="ecmascriptwren">import "./math" for Int, Nums
import "./sort" for Find
import "./seq" for Seq
import "./fmt" for Fmt
 
var primes = Int.primeSieve(1e7)
 
var isTetraPrime = Fn.new { |n|
var count = 0
var prevFact = 1
for (p in primes) {
var limit = p * p
if (count == 0) {
limit = limit * limit
} else if (count == 1) {
limit = limit * p
}
if (limit <= n) {
while (n % p == 0) {
if (count == 4 || p == prevFact) return false
count = count + 1
n = (n/p).floor
prevFact = p
}
} else {
break
}
}
if (n > 1) {
if (count == 4 || n == prevFact) return false
count = count + 1
}
return count == 4
}
 
var highest5 = primes[Find.nearest(primes, 1e5) - 1]
var highest6 = primes[Find.nearest(primes, 1e6) - 1]
Line 732 ⟶ 2,021:
var j = 1e5
for (p in primes) {
// process even numbers first as likely to have most factors
var pf1 = Int.primeFactors(p-2)
varif cond1 = pf1(isTetraPrime.count == 4call(p-1) && !SeqisTetraPrime.hasAdjDupcall(pf1p-2)) {
 
var pf2 = Int.primeFactors(p-1)
var cond2 = pf2.count == 4 && !Seq.hasAdjDup(pf2)
 
var pf3 = Int.primeFactors(p+1)
var cond3 = pf3.count == 4 && !Seq.hasAdjDup(pf3)
 
var pf4 = Int.primeFactors(p+2)
var cond4 = pf4.count == 4 && !Seq.hasAdjDup(pf4)
 
if (cond1 && cond2) {
tetras1.add(p)
if (pf1.contains(7p-1)%7 == 0 || pf2.contains(7p-2)%7 == 0) sevens1 = sevens1 + 1
}
 
if (cond3 && cond4) {
if (isTetraPrime.call(p+1) && isTetraPrime.call(p+2)) {
tetras2.add(p)
if (pf3.contains(7p+1)%7 == 0 || pf4.contains(7p+2)%7 == 0) sevens2 = sevens2 + 1
}
 
Line 838 ⟶ 2,117:
 
=={{header|XPL0}}==
Works on Raspberry Pi.
<syntaxhighlight lang "XPL0">include xpllib; \for Print
<syntaxhighlight lang "XPL0">include xpllib; \for IsPrime, Sort, and Print
 
func Median(A, Len); \Return median value of (sorted) array A
int A, Len, M;
[M:= Len/2;
return if rem(0) then A(M) else (A(M-1) + A(M)) / 2;
];
 
int Have7; \ABoolean: a tetraprime factor is 7
 
procfunc IsTetraprime(N); \Return 'true' if N is a tetraprime
int N;
int Div, Count, Distinct;
Line 861 ⟶ 2,147:
];
 
int Sign, TenPower, TP, Case, N, N0, Count, Count7, Gap, GapMin, GapMax, GapSumGaps;
[Sign:= -1; TenPower:= 100_000;
for TP:= 5 to 7 do
[for Case:= 1 to 2 do \preceding or following neighboring pairs
[Count:= 0; Count7:= 0; N0:= 0; GapMin:= -1>>1; GapMax:= 0; GapSumGaps:= 0;
if TP = 5 then CrLf(0); \100_000
for N:= 3 to TenPower-1 do
Line 879 ⟶ 2,165:
if Have7 then Count7:= Count7+1;
if N0 # 0 then
[GapGaps:= NReallocMem(Gaps, - N0Count*4); \4 = SizeOfInt
ifGaps(Count-2):= GapN < GapMin then GapMin:=- GapN0;
if Gap > GapMax then GapMax:= Gap;
GapSum:= GapSum + Gap;
];
N0:= N;
Line 889 ⟶ 2,173:
N:= N+1;
];
Sort(Gaps, Count-1);
Print("\nFound %,d primes under %,d whose neighboring pair are tetraprimes\n",
Count, TenPower);
Print("of which %,d have a neighboring pair, one of whose factors is 7.\n\n",
Count7);
Print("Minimum gap between %,d primes : %,d\n", Count, GapMinGaps(0));
Print("AverageMedian gap between %,d primes : %,d\n", Count, Median(Gaps, Count-1));
Print("Maximum gap between %,d fix(float(GapSum)/floatprimes : %,d\n", Count, Gaps(Count-1)2));
Print("Maximum gap between %d primes : %,d\n", Count, GapMax);
Sign:= Sign * -1;
];
Line 914 ⟶ 2,198:
 
Minimum gap between 49 primes : 56
AverageMedian gap between 49 primes : 1,891208
Maximum gap between 49 primes : 6,460
 
Line 926 ⟶ 2,210:
 
Minimum gap between 46 primes : 112
AverageMedian gap between 46 primes : 21,004460
Maximum gap between 46 primes : 10,284
 
Line 933 ⟶ 2,217:
 
Minimum gap between 885 primes : 4
AverageMedian gap between 885 primes : 1,119756
Maximum gap between 885 primes : 7,712
 
Line 940 ⟶ 2,224:
 
Minimum gap between 866 primes : 4
AverageMedian gap between 866 primes : 1,146832
Maximum gap between 866 primes : 10,284
 
Line 946 ⟶ 2,230:
of which 5,176 have a neighboring pair, one of whose factors is 7.
 
Minimum gap between 1081510,815 primes : 4
AverageMedian gap between 1081510,815 primes : 924648
Maximum gap between 1081510,815 primes : 9,352
 
Found 10,551 primes under 10,000,000 whose neighboring pair are tetraprimes
of which 5,069 have a neighboring pair, one of whose factors is 7.
 
Minimum gap between 1055110,551 primes : 4
AverageMedian gap between 1055110,551 primes : 947660
Maximum gap between 1055110,551 primes : 10,284
</pre>
Aspen138
337

edits

Retrieved from "https://rosettacode.org/wiki/Special:MobileDiff/345345...358652"