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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
EXAMPLESCLOSE ALL
Basic Examples   (1)
PrimeQ indicates that 1093 is prime:
ProvablePrimeQ gives the same result, but it has generated a certificate:
Needs["PrimalityProving`"]
PrimeQ indicates that 1093 is prime:
In[2]:=
Click for copyable input
Out[2]=
ProvablePrimeQ gives the same result, but it has generated a certificate:
In[3]:=
Click for copyable input
Out[3]=
Scope   (2)
ProvablePrimeQ works on arbitrarily large numbers:
ProvablePrimeQ automatically threads over lists:
Options   (2)
Use the option "Certificate"->True to view the certificate directly:
A random prime:
Progress messages are printed with "PrimeQMessages" -> True:
Properties & Relations   (1)
Here is a random prime:
If ProvablePrimeQ has returned a result, use PrimeQCertificate to print the certificate:
With "Certificate"->True, ProvablePrimeQ repeats the Atkin-Morain primality test:
Possible Issues   (1)
A certificate cannot be generated for -1, 0 or 1:
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