# Difference between revisions of "Semiprime"

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[[Encryption]] algorithms, including [[RSA]] [[encryption]], typically rely on special large semiprimes. A table of such semiprimes is listed at [http://mathworld.wolfram.com/Semiprime.html MathWorld semiprime]. | [[Encryption]] algorithms, including [[RSA]] [[encryption]], typically rely on special large semiprimes. A table of such semiprimes is listed at [http://mathworld.wolfram.com/Semiprime.html MathWorld semiprime]. | ||

− | Interestingly, though the [[Goldbach conjecture]] in its full form remains intractable to current techniques, a related related result for semiprimes has been known since the 1970s. The work of Chen Jingrun showed that every even number is either the sum of two primes, or the sum of a prime and a semiprime. | + | Interestingly, though the [[Goldbach conjecture]] in its full form remains intractable to current techniques, a related related result for semiprimes has been known since the 1970s. The work of Chen Jingrun showed that every even number is either the sum of two primes, or the sum of a prime and a semiprime. It has also been shown that there exist infinitely many primes ''p'' such that ''p''+2 is either a prime or a semiprime. Primes that have this property are known as Chen primes.<ref>http://mathworld.wolfram.com/ChenPrime.html</ref> |

+ | ==References== | ||

+ | <references /> | ||

==External Links== | ==External Links== | ||

*[http://www.research.att.com/~njas/sequences/A001358 Semiprimes] at the OEIS | *[http://www.research.att.com/~njas/sequences/A001358 Semiprimes] at the OEIS | ||

[[Category:Number Theory]] | [[Category:Number Theory]] |

## Revision as of 16:54, October 18, 2009

A **semiprime** is the product of two (possibly equal) prime numbers.

Other names for a "semiprime" are biprime, 2-almost prime, and pq-number.

Encryption algorithms, including RSA encryption, typically rely on special large semiprimes. A table of such semiprimes is listed at MathWorld semiprime.

Interestingly, though the Goldbach conjecture in its full form remains intractable to current techniques, a related related result for semiprimes has been known since the 1970s. The work of Chen Jingrun showed that every even number is either the sum of two primes, or the sum of a prime and a semiprime. It has also been shown that there exist infinitely many primes *p* such that *p*+2 is either a prime or a semiprime. Primes that have this property are known as Chen primes.^{[1]}

## References

## External Links

- Semiprimes at the OEIS