pseudoprime

English

Etymology

Etymology tree

Pre-Greekder.?

Ancient Greek ψεύδω (pseúdō)

Proto-Indo-European *-os

Proto-Indo-European *-ēs

Proto-Hellenic *-ēs

Ancient Greek -ης (-ēs)

Ancient Greek -ής (-ḗs)

Ancient Greek ψευδής (pseudḗs)der.

Middle English pseudo-

English pseudo-

English prime

English pseudoprime

From pseudo- + prime.

Pronunciation

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Noun

pseudoprime (plural pseudoprimes)

1. (mathematics) An integer that possesses at least one characteristic of a prime number without actually being prime. The characteristic is typically chosen to make such "false primes" very rare.
2. (mathematics, specifically) A Fermat pseudoprime; a composite integer n satisfying $b^{n-1}\equiv 1(\mathrm{mod}n)$ for some integer b such that b > 1.

Usage notes

In the sense of a Fermat pseudoprime, if no base is specified, base two is assumed. Integers that satisfy the congruence for a particular b are referred to as "pseudoprimes to base b" or "pseudoprimes to the base b."

Derived terms

• Fermat pseudoprime

Adjective

pseudoprime (not comparable)

1. Being such an integer.