Thread: "New" primality test/check View Single Post
2018-03-12, 19:07   #252
CRGreathouse

Aug 2006

32·5·7·19 Posts

Quote:
 Originally Posted by gophne I would like still to have a crack at offering a "proof" for the twin prime conjecture shortly, in a month or two for te most. I am not sure if posting in the "mersenneforum.org>Extra Stuff>Bloggorrhea>gophne>"New" primality test/check" would be the right forum to do so (although I believe it would be).
Yes, that would be fine. You could also use misc math, but I think this would be better.

A new thread would be better than re-using this one, I think.

Quote:
 Originally Posted by gophne I have stated from the first time that I joined the mersenne forum to air my "discovery" of the sum of consecutive prime "sums" generates very "smooth" curves which lends itself to being "predictive" probably to more or less than of the trivial formula for the gap between primes of log N
My hope is that we can help hone that general idea into a concrete statement and some theorems you can claim.

Quote:
 Originally Posted by gophne I did not make many friends as well with my "reverse algorithm" of the mersenne numbers being divisible by the mersenne index -2 relationship, which was shown to be a variation/copy of Fermat's Little theorem, including the false positives!
Everyone here has had the experience of re-discovering results, we don't mind that part. But you made grandiose claims about the algorithm which did not hold up to casual scrutiny, and that makes us worry about your other claims. If nothing else it should be a wake-up call reminding you of the importance of writing your proof carefully.

Quote:
 Originally Posted by gophne I have also offered a "primality" algorithm which revolves around doubling of an odd number to be tested for primality . If no odd number smaller than the number being tested shares a common factor with the "sum of the that odd number with double the number being tested", then the number being tested is a prime number. This "algorithm" has been highligthed as a "variation" of "trial division", but more cumbersome in computer calculation time!
Well... that is a very inefficient algorithm, hundreds of thousands of times slower than trial division at 9 digits (and quickly growing worse). But perhaps you had some other reason for presenting it other than efficiency.

Quote:
 Originally Posted by gophne So needless to say that besides the attempted proof of the "Twin prime conjecture", I am also working on an alternative primality check to the Lucas-Lehmer, which is showing great promise- I am working on the complexity of the algorithm at very large values in the ranges of the higher mersenne primes. The algorithm is a sieve/formulaic hybrid which I am hoping to air on this forum as well at some point, if I am not debarred from the Site before that as a Swengali!
You'll need very careful proofs for both. I wish you the best.

Quote:
 Originally Posted by gophne This algorithm has proven to be true for the lower mersenne numbers primes (my assertion only), so is most likely, or shall I be bold and say "definitely", true for the higher mersenne numbers as well, I am just not sure of the complexity of the algorithm in terms of computational time required at the top levels/magnitude of the known mersenne primes.
How many non-Mersenne exponents have you tested it on?

"Definitely" is far too strong in any case; even if you had tested it on billions it would only be enough evidence to think it a probable prime test. But such tests definitely exist, and who knows, it might even be a primality test -- just be scrupulous in your proof!