Safe and Sophie Germain primes

Safe and Sophie Germain 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.

A prime number p is Sophie Germain prime if 2p + 1 is also prime.

See the same at Safe_primes_and_unsafe_primes

The number 2p + 1 associated with a Sophie Germain prime is called a safe prime.

Task

Generate the first   50   Sophie Germain prime numbers.

ALGOL 68

Library: ALGOL 68-primes

<lang algol68>BEGIN # find some Sophie Germain primes: primes p such that 2p + 1 is prime #

   PR read "primes.incl.a68" PR
   []BOOL prime = PRIMESIEVE 10 000;              # hopefully, enough primes #
   INT sg count := 0;
   FOR p WHILE sg count < 50 DO    # find the first 50 Sophie Germain primes #
       IF prime[ p ] THEN
           IF prime[ p + p + 1 ] THEN
               print( ( " ", whole( p, -6 ) ) );
               IF ( sg count +:= 1 ) MOD 12 = 0 THEN print( ( newline ) ) FI
           FI
       FI
   OD

END</lang>

Output:

      2      3      5     11     23     29     41     53     83     89    113    131
    173    179    191    233    239    251    281    293    359    419    431    443
    491    509    593    641    653    659    683    719    743    761    809    911
    953   1013   1019   1031   1049   1103   1223   1229   1289   1409   1439   1451
   1481   1499

FreeBASIC

<lang freebasic>function isprime(n as integer) as boolean

   if n < 2 then return false
   if n < 4 then return true
   if n mod 2 = 0 then return false
   dim as uinteger i = 1
   while i*i<=n
       i+=2
       if n mod i = 0 then return false
   wend
   return true

end function

function is_sg( n as integer ) as boolean

   if not isprime(n) then return false
   return isprime(2*n+1)

end function

dim as uinteger c = 1, i = 1 print "2 "; while c<50

   i+=2
   if is_sg(i) then
       print i;"  ";
       c+=1
       if c mod 10 = 0 then print
   end if

wend</lang>

Output:

2  3  5  11  23  29  41  53  83  89
113  131  173  179  191  233  239  251  281  293  
359  419  431  443  491  509  593  641  653  659  
683  719  743  761  809  911  953  1013  1019  1031  
1049  1103  1223  1229  1289  1409  1439  1451  1481  1499

jq

Works with: jq

Works with gojq, the Go implementation of jq

See e.g. #Find_adjacent_primes_which_differ_by_a_square_integer#jq for suitable implementions of `is_prime/0` and `primes/0` as used here. <lang jq>limit(50; primes | select(2*. + 1|is_prime))</lang>

Output:

2
3
5
...
1451
1481
1499

Julia

<lang julia>using Primes

for (i, p) in enumerate(filter(x -> isprime(2x + 1), primes(1500)))

   print(lpad(p, 5), i % 10 == 0 ? "\n" : "")

end

</lang>

Output:

    2    3    5   11   23   29   41   53   83   89
  113  131  173  179  191  233  239  251  281  293
  359  419  431  443  491  509  593  641  653  659
  683  719  743  761  809  911  953 1013 1019 1031
 1049 1103 1223 1229 1289 1409 1439 1451 1481 1499

PARI/GP

<lang parigp>issg(n)=if(isprime(n)&&isprime(1+2*n),1,0) c = 0 n = 2 while(c<50,if(issg(n),print(n);c=c+1);n=n+1)</lang>

Perl

<lang perl>#!/usr/bin/perl

use strict; # https://rosettacode.org/wiki/Safe_and_Sophie_Germain_primes use warnings; use ntheory qw( forprimes is_prime);

my @want; forprimes { is_prime(2 * $_ + 1) and (50 == push @want, $_)

 and print("@want\n" =~ s/.{65}\K /\n/gr) + exit } 2, 1e9;</lang>

Output:

2 3 5 11 23 29 41 53 83 89 113 131 173 179 191 233 239 251 281 293
359 419 431 443 491 509 593 641 653 659 683 719 743 761 809 911 953
1013 1019 1031 1049 1103 1223 1229 1289 1409 1439 1451 1481 1499

Phix

with javascript_semantics
function sophie_germain(integer p)
    return is_prime(2*p+1)
end function

sequence res = {}
integer n = 1
while length(res)<50 do
    integer p = get_prime(n)
    if sophie_germain(p) then res &= p end if
    n += 1
end while
printf(1,"First 50: %s\n",{join(shorten(apply(res,sprint),"",5))})

Output:

First 50: 2 3 5 11 23 ... 1409 1439 1451 1481 1499

Raku

<lang perl6>put join "\n", (^∞ .grep: { .is-prime && ($_*2+1).is-prime } )[^50].batch(10)».fmt: "%4d";</lang>

Output:

   2    3    5   11   23   29   41   53   83   89
 113  131  173  179  191  233  239  251  281  293
 359  419  431  443  491  509  593  641  653  659
 683  719  743  761  809  911  953 1013 1019 1031
1049 1103 1223 1229 1289 1409 1439 1451 1481 1499

Wren

Library: Wren-math

Library: Wren-seq

Library: Wren-fmt

<lang ecmascript>import "./math" for Int import "./seq" for Lst import "./fmt" for Fmt

var sgp = [] var p = 2 var count = 0 while (count < 50) {

   if (Int.isPrime(p) && Int.isPrime(2*p+1)) {
       sgp.add(p)
       count = count + 1
   }
   p = (p != 2) ? p + 2 : 3

} System.print("The first 50 Sophie Germain primes are:") for (chunk in Lst.chunks(sgp, 10)) Fmt.print("$,5d", chunk)</lang>

Output:

The first 50 Sophie Germain primes are:
    2     3     5    11    23    29    41    53    83    89
  113   131   173   179   191   233   239   251   281   293
  359   419   431   443   491   509   593   641   653   659
  683   719   743   761   809   911   953 1,013 1,019 1,031
1,049 1,103 1,223 1,229 1,289 1,409 1,439 1,451 1,481 1,499

XPL0

<lang XPL0>func IsPrime(N); \Return 'true' if N is a prime number int N, I; [for I:= 2 to sqrt(N) do

   if rem(N/I) = 0 then return false;

return true; ];

int N, Count; [N:= 2; Count:= 0; repeat if IsPrime(N) & IsPrime(2*N+1) then

           [IntOut(0, N);  ChOut(0, 9\tab\);
           Count:= Count+1;
           if rem(Count/10) = 0 then CrLf(0);
           ];
       N:= N+1;

until Count >= 50; ]</lang>

Output:

2       3       5       11      23      29      41      53      83      89      
113     131     173     179     191     233     239     251     281     293     
359     419     431     443     491     509     593     641     653     659     
683     719     743     761     809     911     953     1013    1019    1031    
1049    1103    1223    1229    1289    1409    1439    1451    1481    1499