Probable Prime

A probable prime is a number satisfying Fermat's little theorem (or some other primality test) for some nontrivial base. A probable prime which is shown to be composite is called a pseudoprime; otherwise, it is a (true) prime.

As of May 2024, the largest known probable primes are the repunit primes


which have 8177207 and 5794777 decimal digits, respectively (Lifchitz and Lifchitz).

Additional large known probable primes include the Wagstaff primes (2^(13347311)+1)/3 and (2^(13372531)+1)/3 (both found by R. Propper in Sep. 2013 and which have 4017941 and 4025533 decimal digits, respectively) and the "dual Sierpinski numbers" 2^n+k (Moore 2009) given by 2^(9092392)+40291 and 2^(5146295)+41693 (which have 2737083 and 1549190 decimal digits, respectively) (Lifchitz and Lifchitz).

See also

Gigantic Prime, Large Number, Primality Certificate, Primality Test, Prime Number, Pseudoprime, Titanic Prime, Wagstaff Prime

Explore with Wolfram|Alpha


Lifchitz, H. and Lifchitz, R. "PRP Records: Probable Primes Top 10000.", P. "Welcome to 'Five or Bust!' " Oct. 8, 2009.

Referenced on Wolfram|Alpha

Probable Prime

Cite this as:

Weisstein, Eric W. "Probable Prime." From MathWorld--A Wolfram Web Resource.

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