Strong pseudoprime

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A strong pseudoprime is an Euler pseudoprime with a special property:

A composite number (where is odd) is a strong pseudoprime to a base if:

or
  • if

The first condition is stronger.

Properties

  • Every strong pseudoprime is also an Euler pseudoprime.
  • Every strong pseudoprime is odd, because every Euler pseudoprime is odd.
  • If a strong pseudoprime is pseudoprime to a base in , than is pseudoprime to a base in and vice versa.
  • There exist Carmichael numbers that are also strong pseudoprimes.

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