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. Among products of two individually known primes, the largest is the square of the largest known prime number.
A formula for the number of semiprimes less than or equal to 
is given for 
by
![pi^((2))(x)=sum_(k=1)^(pi(sqrt(x)))[pi(x/(p_k))-k+1],](/images/equations/Semiprime/NumberedEquation1.svg) |
(1)
|
where 
is the prime
counting function and 
is the 
th prime number
(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 primes, the following congruence
is satisfied:
 |
(2)
|
In addition, the totient function satisfies the simple identity
 |
(3)
|
Generating provable semiprimes of more than 250 digits by methods other than multiplying two primes together is nontrivial. One method is
prime factorization. From the Cunningham project,
and 
are factored semiprimes with 274 and 301 digits. Similarly,
the indices of Mersenne numbers that give semiprimes
are 4, 9, 11, 23, 37, 41, 49, 59, 67, 83, ... (OEIS A085724).
As of 2022, the largest known indices giving semiprimes are 1427 and 1487.
Reble (2005) showed how an elliptic pseudo-curve and the Goldwasser-Kilian ECPP theorem could generate a 1084-digit provable semiprime without a known prime factorization. Vitto (2021) subsequently found a backdoor strategy, factored Reble's 1084-digit semiprime, and introduced a new method for creating a semiprime certificate that is at least as secure as for random semiprimes of same size.
Encryption algorithms such as RSA encryption rely on special large numbers that have as their factors two large primes. The following table lists some special semiprimes that are the product of two large (distinct) primes.
 | digits in  | digits in  | digits in  |
 | 45 | 23 | 23 |
 | 49 | 21 | 28 |
 | 51 | 22 | 29 |
 | 54 | 23 | 32 |
 | 54 | 25 | 29 |
 | 55 | 25 | 31 |
 | 64 | 32 | 32 |
| RSA-129 | 129 | 64 | 65 |
| RSA-140 | 140 | 70 | 70 |
| RSA-155 | 155 | 78 | 78 |
