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# cryptography...why primes?

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i''m just beginning to learn about cryptography.. and i''m wondering..why primes? why can''t you just have a huge odd number...i mean...wouldn''t computers have trouble factoring that? for example you have 390283490829023903908420....i''m pretty sure it isn''t a prime number, but how would you find the exact factorization? Where is my logic flawed?

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You want a number that is the product of two large primes
or else you run the risk of it being easily factored.

The brute-force method would be to keep dividing by 2, 3, 5, 7...etc.

If your arbitrary number has small prime factors, it''ll be
easy to factor it.

Kami no Itte ga ore ni zettai naru!

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oooooh i see now..erg...these dumb primes.

so how do they keep these primes? in a huge table or database? do tehy randomly pick one when they need to use a prime?

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The first few Google hits returned the Prime Page.

Kami no Itte ga ore ni zettai naru!

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Basically, you pick a random number, and you check if it''s prime. If it isn''t, you pick another one. Surprisingly, it doesn''t take all that long. Although definite tests for primality exist, they''re rather time-consuming, so you generally use a much faster set of tests that says whether a number is almost certainly prime.

"Sneftel is correct, if rather vulgar." --Flarelocke

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