primality test binary

Question

I'm generating numbers using a Java program (BigIntegers) and I want to know if there's a binary readily available that I could use to run primality tests on the numbers generated.... suppose I feed them through a pipe from my java program into the binary. Is it out there? I'm trying to find packages for aks on apt but I see nothing "straightforward", only libs that I could use to program stuff (like, based on GMP).

Answer 1

openssl

The program openssl does primality tests:

$ a=31
$ openssl prime 31
1F (31) is prime

$ openssl prime 18446744073709551557      
FFFFFFFFFFFFFFC5 (18446744073709551557) is prime

The command is listed with help (openssl help):

$ openssl help 2>&1 | grep prime
pkeyparam         pkeyutl           prime             rand

And the details of the actual command are given by (-help or --help):

$ openssl prime -help
Usage: prime [options] [number...]
  number Number to check for primality
 -help         Display this summary
 -hex          Hex output
 -generate     Generate a prime
 -bits +int    Size of number in bits
 -safe         When used with -generate, generate a safe prime
 -checks +int  Number of checks

Very long numbers are also possible (2^521)-1 (Mersenne number with 157 decimal digits):

$ time openssl prime $(BC_LINE_LENGTH=0 bc <<<'2^521-1')
1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
(6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151)
is prime

real    0m0.042s

Two other utilities not connected to openssl but related to primes are:

---

Primes and factor:

primes - generate primes in a range factor - factor numbers

$  echo $(primes 10 50)
11 13 17 19 23 29 31 37 41 43 47

$ openssl prime 11 13 17 19 23 29 31 37 41 43 47
B (11) is prime
D (13) is prime
11 (17) is prime
13 (19) is prime
17 (23) is prime
1D (29) is prime
1F (31) is prime
25 (37) is prime
29 (41) is prime
2B (43) is prime
2F (47) is prime

$ factor 11 13 17 19 23 29 31 37 41 43 47
11: 11
13: 13
17: 17
19: 19
23: 23
29: 29
31: 31
37: 37
41: 41
43: 43
47: 47

$ factor 18446744073709551557
18446744073709551557: 18446744073709551557

$ factor 18446744073709551559
18446744073709551559: 41 163 269 8807 1165112831

Quite close to the max (signed) 64 bit integer number:

$ printf '%X\n' 18446744073709551559 $(( (2<<63) - 1 ))
FFFFFFFFFFFFFFC7
FFFFFFFFFFFFFFFF

Answer 2

There is a primesieve-bin package:

$ sudo apt install primesieve-bin
$ primesieve  20 -p
2
3
5
7
11
13
17
19

to check that a number is prime, you could do:

$ test $(primesieve  11 -p | tail -1) -eq 11
$ echo $?
0

$ test $(primesieve  12 -p | tail -1) -eq 12
$ echo $?
1

EDIT: Not recommended since openssl primes is much faster for that task (as pointed out in the comments).