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).

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.