New test for Mersenne prime

[science_man_88]

Originally Posted by CRGreathouse

The squarings and modulus you speak of are parts of a single modular squaring (which may not have distinct "squaring" and "reducing" steps). The subtractions are cheap compared to the squarings. Technically, squaring is different from (easier than) multiplication, but at a minimum a test designed to supplant LL can't do more than p full-length multiplications, because those alone would take longer than the LL.

I have a possible property of most (exception when using in my idea as one of the exponents.)of the confirmed order exponents I think but it may be nothing but it does work for all exponents up to according to the values of the exponents given at: http://primes.utm.edu/mersenne/

PS. looks to have failed as a definitive test!

[billymac00]

Pari can be used, just use modular exponentiation using repeated squaring. On my pathetic computer things really slow down beginning at exp=756839. I haven't framed the timing as a f{exp size}. If someone has superior computing capability I would be curious as to their timing for 756839, I can supply the script.