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).
