semiprime
A composite number which is the product of two (possibly equal) primes is called semiprime. Such numbers are sometimes also called 2-almost primes. For example:
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1 is not a semiprime because it is not a composite number or a prime,
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2 is not a semiprime, as it is a prime,
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4 is a semiprime, since ,
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8 is not a semiprime, since it is a product of three primes (),
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2003 is not a semiprime, as it is a prime,
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2005 is a semiprime, since ,
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2007 is not a semiprime, since it is a product of three primes ().
The first few semiprimes are (http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=001358Sloane’s sequence A001358 ). The Moebius function for semiprimes can be only equal to 0 or 1. If we form an integer sequence of values of for semiprimes we get a binary sequence: . (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 . (http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=001248Sloane’s sequence A001248 ). The Moebius function for the squares of primes is always equal to 0 as it is equal to 0 for all squares.
Title | semiprime |
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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 |