PRIMALITY PROVING PACKAGE SYMBOL
- To use ProvablePrimeQ, you first need to load the Primality Proving Package using Needs["PrimalityProving`"].
- When ProvablePrimeQ[n] returns True, then n is prime based on the Pratt certificate of primality or the Atkin–Morain certificate of primality.
- ProvablePrimeQ should not be used as a replacement for PrimeQ, as PrimeQ is several orders of magnitude faster. Instead, use ProvablePrimeQ to certify the results of PrimeQ when needed.
- The following options can be given:
|"SmallPrime"||1050||lower bound for using the Atkin–Morain test|
|"Certificate"||False||whether to print a certificate|
|"PollardPTest"||Automatic||whether to use the Pollard method|
|"PollardRhoTest"||Automatic||whether to use the Pollard method|
|"TrialDivisionLimit"||Automatic||number of primes to use in trial division|
|"PrimeQMessages"||False||whether progress is to be monitored|
PrimeQ indicates that 1093 is prime:
ProvablePrimeQ gives the same result, but it has generated a certificate: