Pseudoprimes and Fermat Numbers
Like composite numbers of the form 2p − 1, every composite Fermat number is a strong pseudoprime to base 2. Because all strong pseudoprimes to base 2 are also Fermat pseudoprimes - i.e.
for all Fermat numbers.
Because it is generally believed that all but the first few Fermat numbers are composite, this makes it possible to generate infinitely many strong pseudoprimes to base 2 from the Fermat numbers.
In 1964, Rotkiewicz showed that the product of any number of prime or composite Fermat numbers will be a Fermat pseudoprime to the base 2.
Read more about this topic: Fermat Number
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