pocklington - generate a Pocklington primality certificate for a
prime number
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
This tool takes a prime number and (tries to) generate a
Pocklington primality certificate.
-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*2^n+1. The default output
filename is as if the right number had been given.
- -lucas
<n>
- Generate a certificate for the Mersenne number 2^n-1 using Lucas' test
(more efficient). The default output filename is lucas<n>.v.
- -mersenne
<n>
- Generate a certificate for the Mersenne number 2^n-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.