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A Fermat number is a special positive number. Fermat numbers are named after Pierre de Fermat. The formula that generates them is
where n is a nonnegative integer. The first nine Fermat numbers are (sequence A000215 in OEIS):
As of 2007, only the first 12 Fermat numbers have been completely factored. (written as a product of prime numbers) These factorizations can be found at Prime Factors of Fermat Numbers.