POCKLINGTON

NAME

pocklington - generate a Pocklington primality certificate for a prime number

SYNOPSIS

pocklington [-o filename] prime
pocklington [-o filename] -next num
pocklington [-o filename] -size s
pocklington [-o filename] -proth k n
pocklington [-o filename] -lucas n
pocklington [-o filename] -mersenne n
pocklington [-o filename] -dec filename

DESCRIPTION

This tool takes a prime number and (tries to) generate a Pocklington primality certificate.

OPTIONS

-v Enable verbose mode -o <filename> Prints the proof script in the file named <filename> (otherwise the name depends on the way the prime was given)
<prime>

A prime number. The default output filename is either prime<prime>.v or, if it’s too long, Prime.v

-next <num>

Generate a certificate for the next prime number following <num>. The default output filename is as if the right number had been given.

-size <s>

Generate a certificate for a prime number with at least <s> decimal digits. The default output filename is as if the right number had been given.

-proth <k> <n>

Generate a certificate for the Proth number k*2ˆn+1. The default output filename is as if the right number had been given.

-lucas <n>

Generate a certificate for the Mersenne number 2ˆn-1 using Lucas’ test (more efficient). The default output filename is lucas<n>.v.

-mersenne <n>

Generate a certificate for the Mersenne number 2ˆn-1 using Pocklington’s test. The default output filename is mersenne<n>.v.

-dec <filename>

Generate a certificate for the number given in the file <filename> ; the file should also contain a partial factorization of the predecessor. The output filename is <filename>.v.