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Semiprime

A semiprime, also called a 2-almost prime, biprime (Conway et al. 2008), or -number, is a composite number that is the product of two (possibly equal) primes. The first few are 4, 6, 9, 10, 14, 15, 21, 22, ... (OEIS A001358). The first few semiprimes whose factors are distinct (i.e., the squarefree semiprimes) are 6, 10, 14, 15, 21, 22, 26, 33, 34, ... (OEIS A006881).The square of any prime number is by definition a semiprime. The largest known semiprime is therefore the square of the largest known prime.A formula for the number of semiprimes less than or equal to is given by(1)where is the prime counting function and is the th prime (R. G. Wilson V, pers. comm., Feb. 7, 2006; discovered independently by E. Noel and G. Panos around Jan. 2005, pers. comm., Jun. 13, 2006).The numbers of semiprimes less than for , 2, ... are 3, 34, 299, 2625, 23378, 210035, ... (OEIS A066265).For with and distinct, the following..

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