RSA-2048
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In mathematics, RSA-2048 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge.
Factoring a number means finding all the prime numbers for which it is the numerical product. Prime numbers, such as 2, 3, 5, 7, 11, and 13, are numbers that cannot be evenly divided by any smaller number, except 1. A non-prime, or composite number, can be written as the product of smaller primes, known as its prime factors. 665, for example is the product of the primes 5, 7, and 19. A number has been factored when all of its prime factors have been identified. As the size of the number increases, factoring it becomes exponentially more difficult.
Factoring 100-digit numbers is easily accomplished with today's hardware and algorithms. Factoring numbers of more than 200 digits, however, is not currently feasible. Advances in both computer hardware and number theory are expected to advance the state of the art. One purpose of this contest is to "track" the state of the art in factoring. Large number prime factors are crucial to cryptography, cryptanalysis, and computer and information security.
The largest number ever factored is 663 bits, but the ability to factor RSA-2048 probably won't be achieved for decades.
RSA-2048 has a length of 617 decimal digits. A cash prize of $200,000 USD has been offered by RSA Security for the successful factorisation of this number.
RSA-2048 = 25195908475657893494027183240048398571429282126204032027777137836043662020
70759555626401852588078440691829064124951508218929855914917618450280848912
00728449926873928072877767359714183472702618963750149718246911650776133798
59095700097330459748808428401797429100642458691817195118746121515172654632
28221686998754918242243363725908514186546204357679842338718477444792073993
42365848238242811981638150106748104516603773060562016196762561338441436038
33904414952634432190114657544454178424020924616515723350778707749817125772
46796292638635637328991215483143816789988504044536402352738195137863656439
1212010397122822120720357
External links
- RSA Factoring Challenge: RSA-2048 (http://www.rsasecurity.com/rsalabs/node.asp?id=2093)fr:RSA-2048