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Old 04 April 2014, 08:51 PM
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Richard W Richard W is offline
Join Date: 19 February 2000
Location: High Wycombe, UK
Posts: 26,436

I'm going to have to go and look up some more maths, because (ahem) the details of how prime numbers are used as cryptographic keys has temporarily slipped my mind, but I may as well ask before I do so:

Does finding larger prime numbers even, in itself, help in cryptography, or if somebody said (for example) "Ha! Our algorithm uses a 17,425,170-digit prime number and therefore is absolutely unbreakable!", would the other cryptographers just look at Wikipedia and say "I know what number that is - it's 257885161 - 1" and be able to break the code?

I'm fairly sure the answer is that the larger numbers do still help, but my reasoning is still too large to fit in this margin, so I'm going to wait until I've finished my tea to check it.

(eta) I do know that there are probably many, many other 17,425,170-digit primes than the one that's known, but it would be a reasonable assumption that the one meant would be the known Mersenne prime.
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