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# 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

 (1) (2)

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

Additional large known probable primes include the Wagstaff primes and (both found by R. Propper in Sep. 2013 and which have and decimal digits, respectively) and the "dual Sierpinski numbers" (Moore 2009) given by and (which have and decimal digits, respectively) (Lifchitz and Lifchitz).

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

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## References

Lifchitz, H. and Lifchitz, R. "PRP Records: Probable Primes Top 10000." http://www.primenumbers.net/prptop/prptop.php.Moore, P. "Welcome to 'Five or Bust!' " Oct. 8, 2009. http://www.mersenneforum.org/showthread.php?t=10754.

Probable Prime

## Cite this as:

Weisstein, Eric W. "Probable Prime." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ProbablePrime.html