Thread: Sum and product of factors of a semiprime
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Old November 4th, 2009, 05:23 AM
tonio tonio is offline
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Originally Posted by Bacterius View Post
Hi all, I'm new on this forum (it is great )

I have a maybe-hard maybe-easy question, which is the following (I have worked quite a lot on it but can't find a way around it) :

Say n = pq, with p and q [non-trivial] primes (so n is semiprime)
Now say m = p + q (same values of p and q obviously)

I know "n", but I need "m" (I don't know p or q). Is there a way around this, or is it just impossible ? Isn't there some kind of relation between the product and the sum of the factors of any semiprime ?

Regards.

I wouldn't say "impossible" but as close to it as you can imagine, in particular if the number n is big, and it must be big if you can't find more or less easily its two prime divisors, EVEN after being said it only has two!
This is the reason why we can have some security when paying, working and having fun with a computer: some codes are based precisely in that (for example, the Public one): you can know the number n, but only the receiver of a message knows its prime divisors.
Just for fun, find the prime divisors of 251646847 (i - this is a product of two primes, ii -don't even dream in trying to find a prime that divides this number by hand, lest you'll get a severe hand-and-brain tiredness)

Tonio
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