Re: Probable Prime Number


bassam king karzeddin wrote:


"If, n = (p^2 + q^2) / 2, where, (p, q) are
odd prime numbers, then, (n) has at most three
distinct odd prime numbers factors"

And, It follows as a result another sub conjecture
with above mention conditions :

"If, (50) divides (p^2 +q^2), then the result is a
good probable prime number"



I don't know why do I think that the number of distinct factors of n is not large enough,
So assuming I have made a mistake in previous conjecture about a number of distinct primes, (four instead of three, then my conjecture may hold true

(hopeing to be mistakin again)

You are.


So, restating my conjector as the following

"If, n = (p^2 + q^2) / 2, where, (p, q) are
odd prime numbers, then, (n) has at most four
distinct odd prime numbers factors"

I suggest you try p = (2^89 + 1)/3, q = (2^107+ 1)/3. The
resulting value of n
has 7 (yes, SEVEN) odd prime factors. I am sure that I can find n
with more than 7, if I try.

The number of odd prime factors should be unbounded as p,q --> oo.

Why on Earth would you think otherwise? I suggest that you look up the
Erdos-Kac theorem. Although it does not apply specifically to p^2 +
q^2,
I think its argument could be applied to numbers of that form.

.

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