Fermat number

A number of the form two to the 2 to the nth power, plus one.  In binary notation, a Fermat number is 2n-1 zeroes between an initial and final 1. The first Fermat number is two to the two to the zeroth power, plus one = 3, or 11 in binary.

In 1999, Richard E. Crandall, Ernst W. Mayer, and Jason S. Papadopoulos proved that the 24th Fermat number, two to the two to the 24th power, plus one, which has more than five million digits, is not a prime. Their computation required more than 10¹⁷ computer operations.

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