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).