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semiprime (Definition)

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 $ 4 = 2\cdot 2$,
  • 8 is not a semiprime, since it is a product of three primes ( $ 8 = 2\cdot 2\cdot 2$),
  • 2003 is not a semiprime, as it is a prime,
  • 2005 is a semiprime, since $ 2005 = 5\cdot 401$,
  • 2007 is not a semiprime, since it is a product of three primes ( $ 2007 = 3\cdot 3\cdot 223$).

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, \ldots$ (Sloane's sequence A001358 ). The Moebius function $ \mu(n)$ for semiprimes can be only equal to 0 or 1. If we form an integer sequence of values of $ \mu(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, \ldots$. (Sloane'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, \ldots$. (Sloane's sequence A001248 ). The Moebius function $ \mu(n)$ for the squares of primes is always equal to 0 as it is equal to 0 for all squares.



"semiprime" is owned by drini. [ full author list (3) | owner history (2) ]
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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 MSC11A41 (Number theory :: Elementary number theory :: Primes)

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