FERMAT PRIME

prime number (one not divisible by an integer larger than 1 except itself) of the form 2x + 1, in which x is 2n, n being an integer. On the basis of his knowledge that numbers of this form are prime for values of n from 1 through 4, the 17th-century French mathematician Pierre Fermat conjectured that all numbers of this form are prime. An 18th-century Swiss mathematician, Leonhard Euler, showed this conjecture to be false, for 225 + 1 is not a prime number; in fact it is known that these numbers are not prime for values of n from 5 through 16, placing doubt on the existence of primes of this form for higher values of n.