Fermat number
Pseudoprimes and Fermat numbers

Like composite numbers of the form 2 − 1, every composite Fermat number is a strong pseudoprime to base 2. This is because all strong pseudoprimes to base 2 are also Fermat pseudoprimes – i.e.,

for all Fermat numbers.

In 1904, Cipolla showed that the product of at least two distinct prime or composite Fermat numbers F a F b … F s, {\displaystyle F_{a}F_{b}\dots F_{s},} a > b > ⋯ > s > 1 {\displaystyle a>b>\dots >s>1} will be a Fermat pseudoprime to base 2 if and only if 2 s > a {\displaystyle 2^{s}>a}.
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