preprime

Preprime is a term used in some mathematical and computational writings to denote a concept that is in some sense “before” or “proximate to” a prime. There is no single, widely accepted definition, and the term is not standard in formal number theory. Consequently, interpretations are largely contextual, varying by author or discipline.

One recurring idea is that a preprime is a number that would be prime under a simple modification. Examples offered in various discussions include numbers that become prime if one digit is changed or if a small adjustment is made to their representation. Since these criteria differ between sources, the exact class of preprimes is not fixed.

Another usage describes a preprime as an element that directly precedes a prime in a specific sequence or rendering of the integers. In this sense, a preprime and its successor prime are linked by the rule generating the sequence, though the generating rule is not universal.

In computational contexts, preprime may refer to an initial or preliminary set of candidates considered before performing a full primality test, serving as a filtering stage. As with other uses, this meaning is not standardized and should be checked against the source.

See also: prime, almost prime, semiprime, primality testing. Etymology: from the prefix pre- meaning before, combined with prime.