bases (the Carmichael numbers), there are no composites that are strong pseudoprimes to all bases.

Motivation and first examples

Let us say we want to investigate if is a probable prime (PRP). We pick base and, inspired by Fermat's little theorem, calculate:
: This shows 31697 is a Fermat PRP (base 3), so we may suspect it is a prime. We now repeatedly halve the exponent:
:
:

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