Are there infinitely many composite Fermat numbers?
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Fermat numbers are numbers of the form Fₙ = 2^2^n + 1. Fₙ is prime for n=0 through n=4, with F₄ = 65537. No other Fermat primes are known, but it is possible that there are more, even infinitely many. In fact, it is even possible that only finitely many Fermat numbers are composite.
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