semiprime


A composite numberMathworldPlanetmath which is the product of two (possibly equal) primes is called semiprime. Such numbers are sometimes also called 2-almost primes. For example:

  • 1 is not a semiprime because it is not a composite number or a prime,

  • 2 is not a semiprime, as it is a prime,

  • 4 is a semiprime, since 4=22,

  • 8 is not a semiprime, since it is a product of three primes (8=222),

  • 2003 is not a semiprime, as it is a prime,

  • 2005 is a semiprime, since 2005=5401,

  • 2007 is not a semiprime, since it is a product of three primes (2007=33223).

The first few semiprimes are 4,6,9,10,14,15,21,22,25,26,33,34,35,38,39,46,49,51,55,57,58,62, (http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=001358Sloane’s sequence A001358 ). The Moebius function μ(n) for semiprimes can be only equal to 0 or 1. If we form an integer sequence of values of μ(n) for semiprimes we get a binary sequence: 0,1,0,1,1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,1,1,. (http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=072165Sloane’s sequence A072165 ).

All the squares of primes are also semiprimes. The first few squares of primes are then 4,9,25,49,121,169,289,361,529,841,961,1369,1681,1849,2209,2809,3481,3721,4489,5041,. (http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=001248Sloane’s sequence A001248 ). The Moebius function μ(n) for the squares of primes is always equal to 0 as it is equal to 0 for all squares.

Title semiprime
Canonical name Semiprime
Date of creation 2013-03-22 12:49:22
Last modified on 2013-03-22 12:49:22
Owner drini (3)
Last modified by drini (3)
Numerical id 9
Author drini (3)
Entry type Definition
Classification msc 11A41
Synonym semi-prime
Synonym 2-almost prime
Defines almost prime