Definition:Semiprime Number

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A semiprime (number) is an integer which is the product of two (not necessarily distinct) primes.


The sequence of semiprimes begins:

$4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, \ldots$

This sequence is A001358 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Obvious examples: if $p, p_1, p_2$ are prime, then:

$p^2$ is semiprime.
$2 p$ is semiprime.
$p_1 p_2$ is semiprime.

Also known as

A semiprime number is most usually referred to just as a semiprime.

The additional specifier number has been included in its name on $\mathsf{Pr} \infty \mathsf{fWiki}$ so as to provive a convenient means of disambiguation from other objects whose names include the term semiprime.

Some sources refer to a semiprime as an almost-prime.

Some sources hyphenate: semi-prime.

Also see

  • Results about semiprimes can be found here.