 TOPICS  # Probable Prime

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, of course, it is a prime).

As of Sep. 2013, the largest known probable primes are the Wagstaff primes and , both found by R. Propper in Sep. 2013 and which have and decimal digits, respectively. Other large known probable primes are 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