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ProvablePrimeQ

ProvablePrimeQ[n]
gives True if n is provably prime, and False otherwise.
  • 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"1050lower bound for using the Atkin-Morain test
"Certificate"Falsewhether to print a certificate
"PollardPTest"Automaticwhether to use the Pollard p-1 method
"PollardRhoTest"Automaticwhether to use the Pollard Rho method
"TrialDivisionLimit"Automaticnumber of primes to use in trial division
"PrimeQMessages"Falsewhether progress is to be monitored
Needs["PrimalityProving`"]
PrimeQ indicates that 1093 is prime:
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ProvablePrimeQ gives the same result, but it has generated a certificate:
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