Foghorn Leghorn ask:
> As you can see, there are only two numbers (2^4253-3 and 2^11213-3) in
> the table that I have not been able to factor. Both fail the probable
> prime test to base 2. Both of these numbers appear to be worthy
> challenges for any factoring effort. If someone knows of any factors of
> these numbers or an easy way to find them, then I'd be interested in
> hearing about it. Are there any rules for these numbers analagous to the
> rules for prime factors of Mersenne numbers?
If a prime q divides 2^(odd exponent) - 3, then 6 is a quadratic
residue modulo q. q must be congruent to 1, 5, 19, or 23 (mod 24).
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