Re: Probable Prime Number


bassam king karzeddin wrote:
Dear All

I would like to introduce the following conjecture about prime factorization without having a proof or a counter example or a reference.

What is it that compels cranks to put forth such conjectures without
even bothering to
test their "conjecture"????


The Conjecture:

"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"


It is nonsense. I found a counter-example on my FIRST try.
Hint: let p = (2^89+1)/3 and q= (2^107+1)/3. n has 7 (SEVEN!)
prime 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"

If by "result", you mean quotient, then this conjecture is trivially
false as well.

.

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