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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:
- 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
 ,
- 8 is not a semiprime, since it is a product of three primes (
 ),
- 2003 is not a semiprime, as it is a prime,
- 2005 is a semiprime, since
 ,
- 2007 is not a semiprime, since it is a product of three primes (
 ).
The first few semiprimes are
 (Sloane'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:
 . (Sloane's sequence A072165 ).
All the squares of primes are also semiprimes. The first few squares of primes are then
 . (Sloane'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.
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"semiprime" is owned by drini. [ full author list (3) | owner history (2) ]
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(view preamble)
| Other names: |
semi-prime, 2-almost prime |
| Also defines: |
almost prime |
| Keywords: |
number theory, primes |
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Cross-references: squares, binary, sequence, integer, Moebius function, numbers, primes, product, composite number
There are 16 references to this entry.
This is version 6 of semiprime, born on 2002-06-28, modified 2006-07-09.
Object id is 3145, canonical name is Semiprime.
Accessed 8548 times total.
Classification:
| AMS MSC: | 11A41 (Number theory :: Elementary number theory :: Primes) |
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Pending Errata and Addenda
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