In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers. Because there are infinitely many prime numbers, there are also infinitely many semiprimes. Semiprimes are also called biprimes, since they include two primes, or second numbers, by analogy with how "prime" means "first". Alternatively non-prime semiprimes are called almost-prime numbers, specifically the "2-almost-prime" biprime and "3-almost-prime" triprime.

The semiprimes less than 100 are:

4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, and 95 (sequence A001358 in the OEIS)

Semiprimes that are not square numbers are called discrete, distinct, or squarefree semiprimes:

6, 10, 14, 15, 21, 22, 26, 33, 34, 35, 38, 39, 46, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, ... (sequence A006881 in the OEIS)

The semiprimes are the case ${\displaystyle k=2}$ of the ${\displaystyle k}$-almost primes, numbers with exactly ${\displaystyle k}$ prime factors. However some sources use "semiprime" to refer to a larger set of numbers, the numbers with at most two prime factors (including unit (1), primes, and semiprimes). These are:

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 46, 47, 49, ... (sequence A037143 in the OEIS)

A semiprime counting formula was discovered by E. Noel and G. Panos in 2005. Let ${\displaystyle \pi _{2}(n)}$ denote the number of semiprimes less than or equal to n. Then $${\displaystyle \pi _{2}(n)=\sum _{k=1}^{\pi \left({\sqrt {n}}\right)}\left[\pi \left({\frac {n}{p_{k}}}\right)-k+1\right]}$$ where ${\displaystyle \pi (x)}$ is the prime-counting function and ${\displaystyle p_{k}}$ denotes the kth prime.