page_title: Semiprime
section_title: Applications
hierarchical_section_title: Semiprime / Applications
context_page_description: In mathematics, a semiprime is a natural number that is the product of 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.
context_section_description: Semiprimes are highly useful in the area of cryptography and number theory, most notably in public key cryptography, where they are used by RSA and pseudorandom number generators such as Blum Blum Shub. These methods rely on the fact that finding two large primes and multiplying them together (resulting in a semiprime) is computationally simple, whereas finding the original factors appears to be difficult. In the RSA Factoring Challenge, RSA Security offered prizes for the factoring of specific large semiprimes and several prizes were awarded. The original RSA Factoring Challenge was issued in 1991, and was replaced in 2001 by the New RSA Factoring Challenge, which was later withdrawn in 2007.
  In 1974 the Arecibo message was sent with a radio signal aimed at a star cluster. It consisted of  binary digits intended to be interpreted as a  bitmap image. The number  was chosen because it is a semiprime and therefore can be arranged into a rectangular image in only two distinct ways (23 rows and 73 columns, or 73 rows and 23 columns).
caption: The Arecibo message