This article will address the topic of Semiprime from different perspectives, with the aim of delving into its importance and relevance today. Its impact in different areas will be analyzed, as well as its evolution over time. Recent studies and research will be presented that shed light on Semiprime and its implications for society. Likewise, possible future implications will be discussed and new areas of study related to Semiprime will be explored. This article seeks to provide a comprehensive view of Semiprime and promote debate about its meaning and significance in the contemporary world.
Product of two prime numbers
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".
The semiprimes are the case of the -almost primes, numbers with exactly 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:
Semiprime numbers have no composite numbers as factors other than themselves. For example, the number 26 is semiprime and its only factors are 1, 2, 13, and 26, of which only 26 is composite.
For a squarefree semiprime (with )
the value of Euler's totient function (the number of positive integers less than or equal to that are relatively prime to ) takes the simple form
This calculation is an important part of the application of semiprimes in the RSA cryptosystem.
For a square semiprime , the formula is again simple:
Applications
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).