Re: Pinoy math enthusiast finds fast way to decode RSA encryption

[Thomas Quinot]

Le 2001-02-07, Padmapani S Ganti écrivait :

> I just wanted to add a thing to the prime number which i found
> independently and i do not know whether this has been achieved earlier or
> not but i have a way of proving that every prime is of the form
> (int)sq.root(1+24n)

Not very interesting, since every integer >= 12 is of that form...

let x integer >= 12.
(x+1)^2 = x^2 + 2x + 1 > x^2 + 24
Therefore there is one N = 1 + 24n which satisfies
x^2 <= N < (x+1)^2
ie x <= sqrt (N) < x+1, which is the definition of
x = int (sqrt (N)).

Thomas.

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