Special neighbor primes
Special neighbor primes is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
- Task
Let (p1, p2) are neighbor primes.
Find and show here in base ten if p1+ p2 -1 is prime, where p1, p2 < 100.
11l
F is_prime(n)
I n == 2
R 1B
I n < 2 | n % 2 == 0
R 0B
L(i) (3 .. Int(sqrt(n))).step(2)
I n % i == 0
R 0B
R 1B
V primes = (0.<100).filter(n -> is_prime(n))
L(i) 0 .< primes.len - 1
V p1 = primes[i]
V p2 = primes[i + 1]
I is_prime(p1 + p2 - 1)
print((p1, p2))- Output:
(3, 5) (5, 7) (7, 11) (11, 13) (13, 17) (19, 23) (29, 31) (31, 37) (41, 43) (43, 47) (61, 67) (67, 71) (73, 79)
Action!
INCLUDE "H6:SIEVE.ACT"
INT FUNC GetNextPrime(INT i BYTE ARRAY primes)
DO
i==+1
UNTIL primes(i)
OD
RETURN (i)
PROC Main()
DEFINE MAXPRIME="99"
DEFINE MAX="200"
BYTE ARRAY primes(MAX+1)
INT i,p
Put(125) PutE() ;clear the screen
Sieve(primes,MAX+1)
FOR i=2 TO MAXPRIME
DO
IF primes(i) THEN
p=GetNextPrime(i,primes)
IF p<=MAXPRIME AND primes(i+p-1)=1 THEN
PrintF("%I+%I-1=%I%E",i,p,i+p-1)
FI
FI
OD
RETURN- Output:
Screenshot from Atari 8-bit computer
3+5-1=7 5+7-1=11 7+11-1=17 11+13-1=23 13+17-1=29 19+23-1=41 29+31-1=59 31+37-1=67 41+43-1=83 43+47-1=89 61+67-1=127 67+71-1=137 73+79-1=151
ALGOL 68
Very similar to The ALGOL 68 sample in the Neighbour primes task
BEGIN # find adjacent primes p1, p2 such that p1 + p2 - 1 is also prime #
PR read "primes.incl.a68" PR
INT max prime = 100;
[]BOOL prime = PRIMESIEVE ( max prime * 2 ); # sieve the primes to max prime * 2 #
[]INT low prime = EXTRACTPRIMESUPTO max prime FROMPRIMESIEVE prime; # get a list of the primes up to max prime #
# find the adjacent primes p1, p2 such that p1 + p2 - 1 is prime #
FOR i TO UPB low prime - 1 DO
IF INT p1 plus p2 minus 1 = ( low prime[ i ] + low prime[ i + 1 ] ) - 1;
prime[ p1 plus p2 minus 1 ]
THEN print( ( "(", whole( low prime[ i ], -3 )
, " +", whole( low prime[ i + 1 ], -3 )
, " ) - 1 = ", whole( p1 plus p2 minus 1, -3 )
, newline
)
)
FI
OD
END- Output:
( 3 + 5 ) - 1 = 7 ( 5 + 7 ) - 1 = 11 ( 7 + 11 ) - 1 = 17 ( 11 + 13 ) - 1 = 23 ( 13 + 17 ) - 1 = 29 ( 19 + 23 ) - 1 = 41 ( 29 + 31 ) - 1 = 59 ( 31 + 37 ) - 1 = 67 ( 41 + 43 ) - 1 = 83 ( 43 + 47 ) - 1 = 89 ( 61 + 67 ) - 1 = 127 ( 67 + 71 ) - 1 = 137 ( 73 + 79 ) - 1 = 151
Arturo
primesBelow100: select 1..100 => prime?
loop 1..dec size primesBelow100 'p [
p1: primesBelow100\[p-1]
p2: primesBelow100\[p]
if prime? dec p1 + p2 ->
print ["(" p1 "," p2 ")"]
]
- Output:
( 3 , 5 ) ( 5 , 7 ) ( 7 , 11 ) ( 11 , 13 ) ( 13 , 17 ) ( 19 , 23 ) ( 29 , 31 ) ( 31 , 37 ) ( 41 , 43 ) ( 43 , 47 ) ( 61 , 67 ) ( 67 , 71 ) ( 73 , 79 )
AWK
# syntax: GAWK -f SPECIAL_NEIGHBOR_PRIMES.AWK
BEGIN {
start = 3
stop = 99
old_prime = 2
for (n=start; n<=stop; n++) {
if (is_prime(n) && is_prime(old_prime)) {
sum = old_prime + n - 1
if (is_prime(sum)) {
count++
printf("%d,%d -> %d\n",old_prime,n,sum)
}
old_prime = n
}
}
printf("Special neighbor primes %d-%d: %d\n",start,stop,count)
exit(0)
}
function is_prime(x, i) {
if (x <= 1) {
return(0)
}
for (i=2; i<=int(sqrt(x)); i++) {
if (x % i == 0) {
return(0)
}
}
return(1)
}
- Output:
3,5 -> 7 5,7 -> 11 7,11 -> 17 11,13 -> 23 13,17 -> 29 19,23 -> 41 29,31 -> 59 31,37 -> 67 41,43 -> 83 43,47 -> 89 61,67 -> 127 67,71 -> 137 73,79 -> 151 Special neighbor primes 3-99: 13
BASIC
FreeBASIC
#include"isprime.bas"
function nextprime( n as uinteger ) as uinteger
'finds the next prime after n
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
dim as uinteger p1, p2
for p1 = 3 to 100 step 2
p2 = nextprime(p1)
if isprime(p1) andalso p2<100 andalso isprime( p1 + p2 - 1 ) then
print p1, p2, p1 + p2 - 1
end if
next p1
- Output:
3 5 7 5 7 11 7 11 17 11 13 23 13 17 29 19 23 41 29 31 59 31 37 67 41 43 83 43 47 89 61 67 127 67 71 137 73 79 151
GW-BASIC
10 FOR P = 3 TO 99 STEP 2
20 GOSUB 130
30 IF Q = 0 THEN GOTO 110
40 GOSUB 220
50 IF P2>100 THEN END
60 T = P
70 P = P2 + T - 1
80 GOSUB 130
90 IF Q = 1 THEN PRINT USING "## + ## - 1 = ###";T;P2;P
100 P=T
110 NEXT P
120 END
130 REM tests if a number is prime
140 Q=0
150 IF P=3 THEN Q=1:RETURN
160 I=1
170 I=I+1
180 IF INT(P/I)*I = P THEN RETURN
190 IF I*I<=P THEN GOTO 170
200 Q = 1
210 RETURN
220 REM finds the next prime after P, result in P2
230 IF P = 0 THEN P2 = 2: RETURN
240 IF P<3 THEN P2 = P + 1: RETURN
250 T = P
260 P = P + 1
270 GOSUB 130
280 IF Q = 1 THEN P2 = P: P = T: RETURN
290 GOTO 260
- Output:
3 + 5 - 1 = 7 5 + 7 - 1 = 11 7 + 11 - 1 = 17 11 + 13 - 1 = 23 13 + 17 - 1 = 29 19 + 23 - 1 = 41 29 + 31 - 1 = 59 31 + 37 - 1 = 67 41 + 43 - 1 = 83 43 + 47 - 1 = 89 61 + 67 - 1 = 127 67 + 71 - 1 = 137 73 + 79 - 1 = 151
Tiny BASIC
REM B = SECOND OF THE NEIGBOURING PRIMES
REM C = P + B - 1
REM I = index variable
REM P = INPUT TO NEXTPRIME ROUTINE AND ISPRIME ROUTINE, also first of the two primes
REM T = Temporary variable, multiple uses
REM Z = OUTPUT OF ISPRIME, 1=prime, 0=not
LET P = 1
20 LET P = P + 2
IF P > 100 THEN END
GOSUB 100
IF Z = 0 THEN GOTO 20
GOSUB 120
IF B > 100 THEN END
LET T = P
LET P = P + B - 1
GOSUB 100
LET C = P
LET P = T
IF Z = 0 THEN GOTO 20
PRINT P," + ",B," - 1 = ", C
GOTO 20
100 REM PRIMALITY BY TRIAL DIVISION
LET Z = 1
LET I = 2
110 IF (P/I)*I = P THEN LET Z = 0
IF Z = 0 THEN RETURN
LET I = I + 1
IF I*I <= P THEN GOTO 110
RETURN
120 REM next prime after P
IF P < 2 THEN LET B = 2
IF P = 2 THEN LET B = 3
IF P < 3 THEN RETURN
LET T = P
130 LET P = P + 1
GOSUB 100
IF Z = 1 THEN GOTO 140
GOTO 130
140 LET B = P
LET P = T
RETURN- Output:
3 + 5 - 1 = 7 5 + 7 - 1 = 11 7 + 11 - 1 = 17 11 + 13 - 1 = 23 13 + 17 - 1 = 29 19 + 23 - 1 = 41 29 + 31 - 1 = 59 31 + 37 - 1 = 67 41 + 43 - 1 = 83 43 + 47 - 1 = 89 61 + 67 - 1 = 127 67 + 71 - 1 = 137 73 + 79 - 1 = 151
C
#include<stdio.h>
#include<stdlib.h>
int isprime( int p ) {
int i;
if(p==2) return 1;
if(!(p%2)) return 0;
for(i=3; i*i<=p; i+=2) {
if(!(p%i)) return 0;
}
return 1;
}
int nextprime( int p ) {
int i=0;
if(p==0) return 2;
if(p<3) return p+1;
while(!isprime(++i + p));
return i+p;
}
int main(void) {
int p1, p2;
for(p1=3;p1<=99;p1+=2) {
p2=nextprime(p1);
if(p2<100&&isprime(p1)&&isprime(p2+p1-1)) {
printf( "%d + %d - 1 = %d\n", p1, p2, p1+p2-1 );
}
}
return 0;
}
- Output:
3 + 5 - 1 = 75 + 7 - 1 = 11 7 + 11 - 1 = 17 11 + 13 - 1 = 23 13 + 17 - 1 = 29 19 + 23 - 1 = 41 29 + 31 - 1 = 59 31 + 37 - 1 = 67 41 + 43 - 1 = 83 43 + 47 - 1 = 89 61 + 67 - 1 = 127 67 + 71 - 1 = 137 73 + 79 - 1 = 151
Delphi
Uses the Delphi Prime-Generator Object
procedure SpecialNeighborPrimes(Memo: TMemo);
var I: integer;
var P1,P2: integer;
var Sieve: TPrimeSieve;
begin
Sieve:=TPrimeSieve.Create;
try
{Build more primes than we need}
Sieve.Intialize(200);
{Go through all primes}
for I:=1 to High(Sieve.Primes) do
begin
{Get neighbor primes}
P1:=Sieve.Primes[I-1];
P2:=Sieve.Primes[I];
{only test up to 100}
if P2>=100 then break;
{if P1+P2-1 is prime then display}
if Sieve.Flags[P1 + P2 - 1] then Memo.Lines.Add(Format('(%d, %d)',[P1,P2]));
end;
finally Sieve.Free; end;
end;
- Output:
(3, 5) (5, 7) (7, 11) (11, 13) (13, 17) (19, 23) (29, 31) (31, 37) (41, 43) (43, 47) (61, 67) (67, 71) (73, 79) Elapsed Time: 9.926 ms.
EasyLang
fastfunc isprim num .
i = 3
while i <= sqrt num
if num mod i = 0
return 0
.
i += 2
.
return 1
.
p = 2
for i = 3 step 2 to 99
if isprim i = 1
pp = p
p = i
if isprim (pp + p - 1) = 1
write "(" & pp & " " & p & ") "
.
.
.
- Output:
(2 3) (3 5) (5 7) (7 11) (11 13) (13 17) (19 23) (29 31) (31 37) (41 43) (43 47) (61 67) (67 71) (73 79)
F#
This task uses Extensible Prime Generator (F#)
// Special neighbor primes. Nigel Galloway: August 6th., 2021
pCache|>Seq.pairwise|>Seq.takeWhile(snd>>(>)100)|>Seq.filter(fun(n,g)->isPrime(n+g-1))|>Seq.iter(printfn "%A")
- Output:
(3, 5) (5, 7) (7, 11) (11, 13) (13, 17) (19, 23) (29, 31) (31, 37) (41, 43) (43, 47) (61, 67) (67, 71) (73, 79)
Factor
USING: kernel lists lists.lazy math math.primes
math.primes.lists prettyprint sequences ;
lprimes dup cdr lzip [ sum 1 - prime? ] lfilter
[ second 100 < ] lwhile [ . ] leach
- Output:
{ 3 5 }
{ 5 7 }
{ 7 11 }
{ 11 13 }
{ 13 17 }
{ 19 23 }
{ 29 31 }
{ 31 37 }
{ 41 43 }
{ 43 47 }
{ 61 67 }
{ 67 71 }
{ 73 79 }
Fermat
Func Nextprime(p) =
q:=1;
while not Isprime(p+q)=1 do
q:=q + 1;
od;
p+q.;
for p1 = 3 to 99 by 2 do
p2:=Nextprime(p1);
if p2<100 and Isprime(p1)=1 and Isprime(p1+p2-1) then
!!(p1,' +',p2,' - 1 =',p1+p2-1);
fi;
od;- Output:
3 + 5 - 1 = 7 5 + 7 - 1 = 11 7 + 11 - 1 = 17 11 + 13 - 1 = 23 13 + 17 - 1 = 29 19 + 23 - 1 = 41 29 + 31 - 1 = 59 31 + 37 - 1 = 67 41 + 43 - 1 = 83 43 + 47 - 1 = 89 61 + 67 - 1 = 127 67 + 71 - 1 = 137 73 + 79 - 1 = 151
Go
package main
import (
"fmt"
"rcu"
)
const MAX = 1e7 - 1
var primes = rcu.Primes(MAX)
func specialNP(limit int, showAll bool) {
if showAll {
fmt.Println("Neighbor primes, p1 and p2, where p1 + p2 - 1 is prime:")
}
count := 0
for i := 1; i < len(primes); i++ {
p2 := primes[i]
if p2 >= limit {
break
}
p1 := primes[i-1]
p3 := p1 + p2 - 1
if rcu.IsPrime(p3) {
if showAll {
fmt.Printf("(%2d, %2d) => %3d\n", p1, p2, p3)
}
count++
}
}
ccount := rcu.Commatize(count)
climit := rcu.Commatize(limit)
fmt.Printf("\nFound %s special neighbor primes under %s.\n", ccount, climit)
}
func main() {
specialNP(100, true)
var pow = 1000
for i := 3; i < 8; i++ {
specialNP(pow, false)
pow *= 10
}
}
- Output:
Neighbor primes, p1 and p2, where p1 + p2 - 1 is prime: ( 3, 5) => 7 ( 5, 7) => 11 ( 7, 11) => 17 (11, 13) => 23 (13, 17) => 29 (19, 23) => 41 (29, 31) => 59 (31, 37) => 67 (41, 43) => 83 (43, 47) => 89 (61, 67) => 127 (67, 71) => 137 (73, 79) => 151 Found 13 special neighbor primes under 100. Found 71 special neighbor primes under 1,000. Found 367 special neighbor primes under 10,000. Found 2,165 special neighbor primes under 100,000. Found 14,526 special neighbor primes under 1,000,000. Found 103,611 special neighbor primes under 10,000,000.
Haskell
import Data.List.Split ( divvy )
isPrime :: Int -> Bool
isPrime n
|n == 2 = True
|otherwise = all (\i -> mod n i /= 0 ) [2..limit]
where
limit = floor $ sqrt $ fromIntegral n
solution :: [[Int]]
solution = filter (\subli -> isPrime (head subli + last subli - 1 )) $ divvy 2 1
$ filter isPrime [2..99]
- Output:
[[3,5],[5,7],[7,11],[11,13],[13,17],[19,23],[29,31],[31,37],[41,43],[43,47],[61,67],[67,71],[73,79]]
J
(#~ 1 p: {:"1) 2 (, _1 + +/)\ i.&.(p:inv) 100
3 5 7
5 7 11
7 11 17
11 13 23
13 17 29
19 23 41
29 31 59
31 37 67
41 43 83
43 47 89
61 67 127
67 71 137
73 79 151
jq
Works with gojq, the Go implementation of jq
This entry uses `is_prime` as defined at Erdős-primes#jq.
# Assumes . > 2
def next_prime:
first(range(.+2; infinite) | select(is_prime));
def specialNP($savePairs):
. as $limit
| {p1: 2, p2: 3}
| until( .p2 >= $limit;
if (.p1 + .p2 - 1 | is_prime)
then .pcount += 1
| if $savePairs then .neighbors = .neighbors + [[.p1, .p2]] else . end
else .
end
| .p1 = .p2
| .p2 = (.p1|next_prime)
)
| if $savePairs then {pcount, neighbors} else {pcount} end;
100|specialNP(true)- Output:
{"pcount":13,"neighbors":[[3,5],[5,7],[7,11],[11,13],[13,17],[19,23],[29,31],[31,37],[41,43],[43,47],[61,67],[67,71],[73,79]]}
Julia
using Primes
function specialneighbors(N, savepairs=true)
neighbors, p1, pcount = Pair{Int}[], 2, 0
while (p2 = nextprime(p1 + 1)) < N
if isprime(p2 + p1 - 1)
savepairs && push!(neighbors, p1 => p2)
pcount += 1
end
p1 = p2
end
return neighbors, pcount
end
spn, n = specialneighbors(100)
println("$n special neighbor prime pairs under 100:")
println("p1 p2 p1 + p2 - 1\n--------------------------")
for (p1, p2) in specialneighbors(100)[1]
println(lpad(p1, 2), " ", rpad(p2, 7), p1 + p2 - 1)
end
print("\nCount of such prime pairs under 1,000,000,000: ",
specialneighbors(1_000_000_000, false)[2])
- Output:
13 special neighbor prime pairs under 100: p1 p2 p1 + p2 - 1 -------------------------- 3 5 7 5 7 11 7 11 17 11 13 23 13 17 29 19 23 41 29 31 59 31 37 67 41 43 83 43 47 89 61 67 127 67 71 137 73 79 151 Count of such prime pairs under 1,000,000,000: 6041231
Mathematica /Wolfram Language
p = Prime@Range@PrimePi[100];
Select[Partition[p, 2, 1], Total/*(# - 1 &)/*PrimeQ]
- Output:
{{3, 5}, {5, 7}, {7, 11}, {11, 13}, {13, 17}, {19, 23}, {29, 31}, {31, 37}, {41, 43}, {43, 47}, {61, 67}, {67, 71}, {73, 79}}
Nim
import strutils, sugar
const Max = 100 - 1
func isPrime(n: Positive): bool =
if n == 1: return false
if n mod 2 == 0: return n == 2
for d in countup(3, n, 2):
if d * d > n: break
if n mod d == 0: return false
result = true
const Primes = collect(newSeq):
for n in 2..Max:
if n.isPrime: n
let list = collect(newSeq):
for i in 0..<Primes.high:
let p1 = Primes[i]
let p2 = Primes[i + 1]
if (p1 + p2 - 1).isPrime: (p1, p2)
echo "Found $1 special neighbor primes less than $2:".format(list.len, Max + 1)
echo list.join(", ")
- Output:
Found 13 special neighbor primes less than 100: (3, 5), (5, 7), (7, 11), (11, 13), (13, 17), (19, 23), (29, 31), (31, 37), (41, 43), (43, 47), (61, 67), (67, 71), (73, 79)
PARI/GP
for(p1=1,100,p2=nextprime(p1+1); if(isprime(p1)&&p2<100&&isprime(p1+p2-1),print(p1," ",p2," ",p1+p2-1)))Perl
#!/usr/bin/perl
use strict; # https://rosettacode.org/wiki/Special_neighbor_primes
use warnings;
use ntheory qw( primes is_prime );
my @primes = @{ primes(100) };
for ( 1 .. $#primes )
{
is_prime( $@ = $primes[$_-1] + $primes[$_] - 1 ) and
printf "%2d + %2d - 1 = %3d\n", $primes[$_-1], $primes[$_], $@;
}
- Output:
3 + 5 - 1 = 7 5 + 7 - 1 = 11 7 + 11 - 1 = 17 11 + 13 - 1 = 23 13 + 17 - 1 = 29 19 + 23 - 1 = 41 29 + 31 - 1 = 59 31 + 37 - 1 = 67 41 + 43 - 1 = 83 43 + 47 - 1 = 89 61 + 67 - 1 = 127 67 + 71 - 1 = 137 73 + 79 - 1 = 151
Phix
with javascript_semantics function np(integer n) return is_prime(get_prime(n)+get_prime(n+1)-1) end function function npt(integer p) return filter(tagset(length(get_primes_le(p))-1),np) end function sequence s = npt(100) printf(1,"Found %d special neighbour primes < 100:\n",length(s)) for i=1 to length(s) do integer si = s[i], pi = get_prime(si), pj = get_prime(si+1) printf(1," (%2d,%2d) => %d\n",{pi,pj,pi+pj-1}) end for printf(1,"\n") for i=2 to 7 do integer p = power(10,i), l = length(npt(p)) printf(1,"Found %,d special neighbour primes < %,d\n",{l,p}) end for
- Output:
Found 13 special neighbour primes < 100: ( 3, 5) => 7 ( 5, 7) => 11 ( 7,11) => 17 (11,13) => 23 (13,17) => 29 (19,23) => 41 (29,31) => 59 (31,37) => 67 (41,43) => 83 (43,47) => 89 (61,67) => 127 (67,71) => 137 (73,79) => 151 Found 13 special neighbour primes < 100 Found 71 special neighbour primes < 1,000 Found 367 special neighbour primes < 10,000 Found 2,165 special neighbour primes < 100,000 Found 14,526 special neighbour primes < 1,000,000 Found 103,611 special neighbour primes < 10,000,000
PL/0
PL/0 can only output a single integer per line, so to avoid confusing output, this sample just shows the first prime of each pair.
This is almost identical to the PL/0 sample in the Neighbour primes task
var n, p1, p2, prime;
procedure isnprime;
var p;
begin
prime := 1;
if n < 2 then prime := 0;
if n > 2 then begin
prime := 0;
if odd( n ) then prime := 1;
p := 3;
while p * p <= n * prime do begin
if n - ( ( n / p ) * p ) = 0 then prime := 0;
p := p + 2;
end
end
end;
begin
p1 := 3;
p2 := 5;
while p2 < 100 do begin
n := ( p1 + p2 ) - 1;
call isnprime;
if prime = 1 then ! p1;
n := p2 + 2;
call isnprime;
while prime = 0 do begin
n := n + 2;
call isnprime;
end;
p1 := p2;
p2 := n;
end
end.
- Output:
3
5
7
11
13
19
29
31
41
43
61
67
73
PL/M
... under CP/M (or an emulator)
100H: /* FIND SOME PAIRS OF PRIMES P, Q BETWEEN 1 AND 99 SUCH THAT P + Q -1 */
/* IS ALSO A PRIME */
/* CP/M BDOS SYSTEM CALL AND I/O ROUTINES */
BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END;
PR$CHAR: PROCEDURE( C ); DECLARE C BYTE; CALL BDOS( 2, C ); END;
PR$STRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END;
PR$NL: PROCEDURE; CALL PR$STRING( .( 0DH, 0AH, '$' ) ); END;
PR$NUMBER: PROCEDURE( N );
DECLARE N ADDRESS;
DECLARE V ADDRESS, N$STR( 6 ) BYTE, W BYTE;
V = N;
W = LAST( N$STR );
N$STR( W ) = '$';
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
DO WHILE( ( V := V / 10 ) > 0 );
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
END;
CALL PR$STRING( .N$STR( W ) );
END PR$NUMBER;
/* TASK */
DECLARE FALSE LITERALLY '0';
DECLARE TRUE LITERALLY '0FFH';
DECLARE MAX$LOW$PRIME LITERALLY '99';
DECLARE PRIME ( 200 )BYTE;
/* THE SIZE OF PRIME SHOULD BE AT LEAST MAX$LOW$PRIME DOUBLED */
/* SIEVE THE PRIMES TO MAX$PRIME */
DECLARE ( P, Q, COUNT ) ADDRESS;
PRIME( 1 ) = FALSE; PRIME( 2 ) = TRUE;
DO P = 3 TO LAST( PRIME ) BY 2; PRIME( P ) = TRUE; END;
DO P = 4 TO LAST( PRIME ) BY 2; PRIME( P ) = FALSE; END;
DO P = 3 TO MAX$LOW$PRIME + 1;
IF PRIME( P ) THEN DO;
DO Q = P * P TO LAST( PRIME ) BY P + P; PRIME( Q ) = FALSE; END;
END;
END;
/* FIND AND SHOW THE SPECIAL NEIGHBOUR PRIMES */
COUNT = 0;
P = 2;
Q = 3;
DO WHILE Q < MAX$LOW$PRIME;
IF PRIME( Q ) THEN DO;
DECLARE SNP ADDRESS;
SNP = P + Q - 1;
IF PRIME( SNP ) THEN DO;
/* P AND Q ARE SPECIAL NEIGHBOUR PRIMES */
CALL PR$STRING( .'( $' );
IF P < 10 THEN CALL PR$CHAR( ' ' );
CALL PR$NUMBER( P );
CALL PR$STRING( .' + $' );
IF Q < 10 THEN CALL PR$CHAR( ' ' );
CALL PR$NUMBER( Q );
CALL PR$STRING( .' ) - 1 = $' );
IF SNP < 100 THEN CALL PR$CHAR( ' ' );
IF SNP < 10 THEN CALL PR$CHAR( ' ' );
CALL PR$NUMBER( SNP );
CALL PR$NL;
END;
P = Q;
END;
Q = Q + 2;
END;
EOF- Output:
( 3 + 5 ) - 1 = 7 ( 5 + 7 ) - 1 = 11 ( 7 + 11 ) - 1 = 17 ( 11 + 13 ) - 1 = 23 ( 13 + 17 ) - 1 = 29 ( 19 + 23 ) - 1 = 41 ( 29 + 31 ) - 1 = 59 ( 31 + 37 ) - 1 = 67 ( 41 + 43 ) - 1 = 83 ( 43 + 47 ) - 1 = 89 ( 61 + 67 ) - 1 = 127 ( 67 + 71 ) - 1 = 137 ( 73 + 79 ) - 1 = 151
Python
#!/usr/bin/python
def isPrime(n):
for i in range(2, int(n**0.5) + 1):
if n % i == 0:
return False
return True
def nextPrime(n):
#finds the next prime after n
if n == 0:
return 2
if n < 3:
return n + 1
q = n + 2
while not isPrime(q):
q += 2
return q
if __name__ == "__main__":
for p1 in range(3,100,2):
p2 = nextPrime(p1)
if isPrime(p1) and p2 < 100 and isPrime(p1 + p2 - 1):
print(p1,'\t', p2,'\t', p1 + p2 - 1)
- Output:
3 5 7 5 7 11 7 11 17 11 13 23 13 17 29 19 23 41 29 31 59 31 37 67 41 43 83 43 47 89 61 67 127 67 71 137 73 79 151
Raku
# 20210809 Raku programming solution
for (grep {.is-prime}, 3..*).rotor(2 => -1) -> (\P1,\P2) {
last if P2 ≥ Ⅽ;
($_ = P1+P2-1).is-prime and printf "%2d, %2d => %3d\n", P1, P2, $_
}
- Output:
3, 5 => 7 5, 7 => 11 7, 11 => 17 11, 13 => 23 13, 17 => 29 19, 23 => 41 29, 31 => 59 31, 37 => 67 41, 43 => 83 43, 47 => 89 61, 67 => 127 67, 71 => 137 73, 79 => 151
REXX
A little extra code was added to present the results in a grid-like format.
/*REXX pgm finds special neighbor primes: P1, P2, P1+P2-1 are prime, and P1 and P2<100*/
parse arg hi cols . /*obtain optional argument from the CL.*/
if hi=='' | hi=="," then hi= 100 /*Not specified? Then use the default.*/
if cols=='' | cols=="," then cols= 5 /* " " " " " " */
call genP hi /*build semaphore array for low primes.*/
do p=1 while @.p<hi
end /*p*/; lim= p-1; q= p+1 /*set LIM to prime for P; calc. 2nd HI.*/
#m= # - 1
call genP @.# + @.#m - 1 /*build semaphore array for high primes*/
w= 20 /*width of a number in any column. */
title= ' special neighbor primes: P1, P2, P1+P2-1 are primes, and P1 and P2 < ' ,
commas(hi)
if cols>0 then say ' index │'center(title, 1 + cols*(w+1) )
if cols>0 then say '───────┼'center("" , 1 + cols*(w+1), '─')
found= 0; idx= 1 /*initialize # neighbor primes & index.*/
$= /*a list of neighbor primes (so far).*/
do j=1 to lim; jp= j+1; q= @.jp /*look for neighbor primes within range*/
y= @.j + q - 1; if \!.y then iterate /*is X also a prime? No, then skip it.*/
found= found + 1 /*bump the number of neighbor primes. */
if cols==0 then iterate /*Build the list (to be shown later)? */
$= $ right( @.j','q"──►"y, w) /*add neighbor prime ──► the $ list. */
if found//cols\==0 then iterate /*have we populated a line of output? */
say center(idx, 7)'│' substr($, 2); $= /*display what we have so far (cols). */
idx= idx + cols /*bump the index count for the output*/
end /*j*/
if $\=='' then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/
if cols>0 then say '───────┴'center("" , 1 + cols*(w+1), '─')
say
say 'Found ' commas(found) title
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?
/*──────────────────────────────────────────────────────────────────────────────────────*/
genP: !.= 0; parse arg limit /*placeholders for primes (semaphores).*/
@.1=2; @.2=3; @.3=5; @.4=7; @.5=11 /*define some low primes. */
!.2=1; !.3=1; !.5=1; !.7=1; !.11=1 /* " " " " flags. */
#=5; sq.#= @.# **2 /*number of primes so far; prime². */
/* [↓] generate more primes ≤ high.*/
do j=@.#+2 by 2 to limit /*find odd primes from here on. */
parse var j '' -1 _; if _==5 then iterate /*J ÷ by 5? (right digit).*/
if j//3==0 then iterate; if j//7==0 then iterate /*" " " 3? J ÷ by 7? */
do k=5 while sq.k<=j /* [↓] divide by the known odd primes.*/
if j // @.k == 0 then iterate j /*Is J ÷ X? Then not prime. ___ */
end /*k*/ /* [↑] only process numbers ≤ √ J */
#= #+1; @.#= j; sq.#= j*j; !.j= 1 /*bump # of Ps; assign next P; P²; P# */
end /*j*/; return
- output when using the default inputs:
index │ special neighbor primes: P1, P2, P1+P2-1 are primes, and P1 and P2 < 100 ───────┼────────────────────────────────────────────────────────────────────────────────────────────────────────── 1 │ 3,5──►7 5,7──►11 7,11──►17 11,13──►23 13,17──►29 6 │ 19,23──►41 29,31──►59 31,37──►67 41,43──►83 43,47──►89 11 │ 61,67──►127 67,71──►137 73,79──►151 ───────┴────────────────────────────────────────────────────────────────────────────────────────────────────────── Found 13 special neighbor primes: P1, P2, P1+P2-1 are primes, and P1 and P2 < 100
Ring
load "stdlib.ring"
see "working..." + nl
see "Special neighbor primes are:" + nl
row = 0
oldPrime = 2
for n = 3 to 100
if isprime(n) and isprime(oldPrime)
sum = oldPrime + n - 1
if isprime(sum)
row++
see "" + oldPrime + "," + n + " => " + sum + nl
ok
oldPrime = n
ok
next
see "Found " + row + " special neighbor primes"
see "done..." + nl- Output:
working... Special neighbor primes are: 3,5 => 7 5,7 => 11 7,11 => 17 11,13 => 23 13,17 => 29 19,23 => 41 29,31 => 59 31,37 => 67 41,43 => 83 43,47 => 89 61,67 => 127 67,71 => 137 73,79 => 151 Found 13 special neighbor primes done...
RPL
≪ → max ≪ { } 3 5 DO IF DUP2 + 1 - ISPRIME? THEN DUP2 R→C 4 ROLL SWAP + UNROT END NIP DUP NEXTPRIME UNTIL DUP max ≥ END DROP2 ≫ ≫ 'SNP' STO
100 SNP
- Output:
1: { (3.,5.) (5.,7.) (7.,11.) (11.,13.) (13.,17.) (19.,23.) (29.,31.) (31.,37.) (41.,43.) (43.,47.) (61.,67.) (67.,71.) (73.,79.) }
Ruby
require 'prime'
Prime.each(100).each_cons(2).select{|p1, p2|(p1+p2-1).prime?}.each{|ar| p ar}
- Output:
[3, 5] [5, 7] [7, 11] [11, 13] [13, 17] [19, 23] [29, 31] [31, 37] [41, 43] [43, 47] [61, 67] [67, 71] [73, 79]
Rust
fn is_prime( number : u16 ) -> bool {
let limit : u16 = (number as f32).sqrt( ).floor( ) as u16 ;
(2..=limit).all( | i | number % i != 0 )
}
fn main() {
let primes : Vec<u16> = (2..100).filter( | &d | is_prime( d ) ).collect( ) ;
let prime_slice = &primes[..] ;
let mut iter = prime_slice.windows( 2 ) ;
while let Some( p ) = iter.next( ) {
if is_prime( p[0] + p[1] - 1 ) {
println!("({} , {})" , p[0] , p[1] );
}
}
}
- Output:
(3 , 5) (5 , 7) (7 , 11) (11 , 13) (13 , 17) (19 , 23) (29 , 31) (31 , 37) (41 , 43) (43 , 47) (61 , 67) (67 , 71) (73 , 79)
Sidef
func special_neighbor_primes(upto) {
var list = []
upto.primes.each_cons(2, {|p1,p2|
var n = (p1 + p2 - 1)
if (n.is_prime) {
list << [p1, p2, n]
}
})
return list
}
with (100) {|n|
var list = special_neighbor_primes(n)
say "Found #{list.len} special neighbour primes < n:"
list.each_2d {|p1,p2,q|
printf(" (%2s, %2s) => %s\n", p1, p2, q)
}
}
say ''
for n in (1..7) {
var list = special_neighbor_primes(10**n)
say "Found #{list.len} special neighbour primes < 10^#{n}"
}
- Output:
Found 13 special neighbour primes < n: ( 3, 5) => 7 ( 5, 7) => 11 ( 7, 11) => 17 (11, 13) => 23 (13, 17) => 29 (19, 23) => 41 (29, 31) => 59 (31, 37) => 67 (41, 43) => 83 (43, 47) => 89 (61, 67) => 127 (67, 71) => 137 (73, 79) => 151 Found 2 special neighbour primes < 10^1 Found 13 special neighbour primes < 10^2 Found 71 special neighbour primes < 10^3 Found 367 special neighbour primes < 10^4 Found 2165 special neighbour primes < 10^5 Found 14526 special neighbour primes < 10^6 Found 103611 special neighbour primes < 10^7
Wren
I assume that 'neighbor' primes means pairs of successive primes.
import "./math" for Int
import "./fmt" for Fmt
var max = 1e7 - 1
var primes = Int.primeSieve(max)
var specialNP = Fn.new { |limit, showAll|
if (showAll) System.print("Neighbor primes, p1 and p2, where p1 + p2 - 1 is prime:")
var count = 0
var p3
for (i in 1...primes.where { |p| p < limit }.count) {
var p2 = primes[i]
var p1 = primes[i-1]
if (Int.isPrime(p3 = p1 + p2 - 1)) {
if (showAll) Fmt.print("($2d, $2d) => $3d", p1, p2, p3)
count = count + 1
}
}
Fmt.print("\nFound $,d special neighbor primes under $,d.", count, limit)
}
specialNP.call(100, true)
for (i in 3..7) {
specialNP.call(10.pow(i), false)
}
- Output:
Neighbor primes, p1 and p2, where p1 + p2 - 1 is prime: ( 3, 5) => 7 ( 5, 7) => 11 ( 7, 11) => 17 (11, 13) => 23 (13, 17) => 29 (19, 23) => 41 (29, 31) => 59 (31, 37) => 67 (41, 43) => 83 (43, 47) => 89 (61, 67) => 127 (67, 71) => 137 (73, 79) => 151 Found 13 special neighbor primes under 100. Found 71 special neighbor primes under 1,000. Found 367 special neighbor primes under 10,000. Found 2,165 special neighbor primes under 100,000. Found 14,526 special neighbor primes under 1,000,000. Found 103,611 special neighbor primes under 10,000,000.
XPL0
func IsPrime(N); \Return 'true' if N is a prime number
int N, I;
[if N <= 1 then return false;
for I:= 2 to sqrt(N) do
if rem(N/I) = 0 then return false;
return true;
];
int P, P1, P2;
[P:= 2;
loop [P1:= P;
repeat P:= P+1;
if P >= 100 then quit;
until IsPrime(P);
P2:= P;
if IsPrime(P1+P2-1) then
[IntOut(0, P1); ChOut(0, ^ );
IntOut(0, P2); ChOut(0, ^ );
IntOut(0, P1+P2-1); CrLf(0);
];
];
]- Output:
3 5 7 5 7 11 7 11 17 11 13 23 13 17 29 19 23 41 29 31 59 31 37 67 41 43 83 43 47 89 61 67 127 67 71 137 73 79 151
Categories:
- Draft Programming Tasks
- Prime Numbers
- 11l
- Action!
- Action! Sieve of Eratosthenes
- ALGOL 68
- ALGOL 68-primes
- Arturo
- AWK
- BASIC
- FreeBASIC
- GW-BASIC
- Tiny BASIC
- C
- Delphi
- SysUtils,StdCtrls
- EasyLang
- F Sharp
- Factor
- Fermat
- Go
- Go-rcu
- Haskell
- J
- Jq
- Julia
- Mathematica
- Wolfram Language
- Nim
- PARI/GP
- Perl
- Phix
- PL/0
- PL/M
- Python
- Raku
- REXX
- Ring
- RPL
- Ruby
- Rust
- Sidef
- Wren
- Wren-math
- Wren-fmt
- XPL0