Semiprime

Computer/Terms 2008. 4. 7. 09:46

In mathematics, a semiprime (also called biprime or 2-almost prime, or pq number) is a natural number that is the product of two (not necessarily distinct) prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, ... (sequence A001358 in OEIS).

As of 2007, the largest known semiprime is (2^32,582,657 − 1)^2, which has over 19 million digits. This is the square of the largest known prime. The square of any prime number is a semiprime, so the largest known semiprime will always be the square of the largest known prime, unless the factors of the semiprime are not known. It is conceivable that somebody could find a way to prove a larger number is a semiprime without knowing the two factors, but so far that has only happened for smaller semiprimes.

The value of Euler's totient function for a semiprime n = pq is particularly simple when p and q are distinct:

φ(n) = n + 1 − (p + q).

Reference:
http://en.wikipedia.org/wiki/Semiprime

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