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Semiprime
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==Applications== [[File:Arecibo message bw.svg|thumb|upright=0.4|The [[Arecibo message]]]]Semiprimes are highly useful in the area of [[cryptography]] and [[number theory]], most notably in [[public key cryptography]], where they are used by [[RSA (algorithm)|RSA]] and [[pseudorandom number generator]]s 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 [[integer factorization|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Factoring Challenge was issued in 1991, and was replaced in 2001 by the New RSA Factoring Challenge, which was later withdrawn in 2007.<ref>{{cite web|title=The RSA Factoring Challenge is no longer active|url=http://www.rsa.com/rsalabs/node.asp?id=2092|publisher=RSA Laboratories|archive-url=https://web.archive.org/web/20130727090515/http://www.rsa.com/rsalabs/node.asp?id=2092|archive-date=2013-07-27}}</ref> In 1974 the [[Arecibo message]] was sent with a radio signal aimed at a [[star cluster]]. It consisted of <math>1679</math> binary digits intended to be interpreted as a <math>23 \times 73</math> [[bitmap]] image. The number <math>1679=23\cdot 73</math> 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).<ref>{{cite book|title=The Number Mysteries: A Mathematical Odyssey through Everyday Life|first=Marcus|last=du Sautoy|author-link=Marcus du Sautoy|publisher=St. Martin's Press|year=2011|isbn=9780230120280|page=19|url=https://books.google.com/books?id=snaUbkIb8SEC&pg=PA19}}</ref>
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