[QUOTE=science_man_88;223590]since every (6n+/-1)*p number is a multiple of a number they can't be prime so if 24n+7 hits one it's not prime can we use this to predict which n for 24n+7 are prime and which ones are Mersenne primes ?[/QUOTE]

So you're suggesting that we can rule out numbers as Mersenne primes by trial division? Yes, that's a good method.

[QUOTE=CRGreathouse;223591]So you're suggesting that we can rule out numbers as Mersenne primes by trial division? Yes, that's a good method.[/QUOTE]

sarcasm I'm guessing. this reminds me of something I raised about [url]http://www.research.att.com/~njas/sequences/A002450[/url]

[QUOTE=CRGreathouse]So you're suggesting that we can rule out numbers as Mersenne primes by trial division? Yes, that's a good method.
[/QUOTE]

Hey, CRG! That gives me a good idea about posting in the kook Mersenne prediction thread! :lol:!

[QUOTE=science_man_88;223594]sarcasm I'm guessing.[/QUOTE]

Not sarcasm, just pointing out that this method is well-known. It *is* a good method.

[QUOTE=science_man_88;223594]this reminds me of something I raised about [url]http://www.research.att.com/~njas/sequences/A002450[/url][/QUOTE]

You refer, I assume, to your thread [url=http://mersenneforum.org/showthread.php?t=13566] 6*(4x+1)+1[/url].

I think the fundamental problem here is that you're trying to use properties of the arithmetic sequence 24n + 7 to determine things about 2^p - 1, but 24n + 7 is so fat (contains ~ x/8log(x) primes up to x) that it's hard to say much at all about a sequence as thin as 2^p - 1 (which contains << log(x)/log(log(x)) primes up to x, probably only log(log (x)) primes).

We're looking for needles in haystacks, but you're suggesting looking for needles in an exponentially bigger haystack... conjecturally, a double-exponentially bigger haystack.

[QUOTE=CRGreathouse;223601]Not sarcasm, just pointing out that this method is well-known. It *is* a good method.



You refer, I assume, to your thread [url=http://mersenneforum.org/showthread.php?t=13566] 6*(4x+1)+1[/url].

I think the fundamental problem here is that you're trying to use properties of the arithmetic sequence 24n + 7 to determine things about 2^p - 1, but 24n + 7 is so fat (contains ~ x/8log(x) primes up to x) that it's hard to say much at all about a sequence as thin as 2^p - 1 (which contains << log(x)/log(log(x)) primes up to x, probably only log(log (x)) primes).

We're looking for needles in haystacks, but you're suggesting looking for needles in an exponentially bigger haystack... conjecturally, a double-exponentially bigger haystack.[/QUOTE]

okay but can we turn those n values in 24n+7 that give primes into 2^p-1 numbers is there a way to convert ?

[QUOTE=science_man_88;223603]okay but can we turn those n values in 24n+7 that give primes into 2^p-1 numbers is there a way to convert ?[/QUOTE]

Sure. Just start at 7 and go upward 24 at a time, testing each member for primality. If you find a prime, add 1 and then see if the result is a power of 2. If so, output it; it's a Mersenne prime.

If you can prove primality in time O(log^4 n) then this takes time O(x log^4 x) to find the Mersenne primes up to x. If you pretest with Miller-Rabin, the time drop to O(x log^3 x).

If you use Lucas-Lehmer, it takes time O(log^3 x log log log x).

[QUOTE=CRGreathouse;223616]Sure. Just start at 7 and go upward 24 at a time, testing each member for primality. If you find a prime, add 1 and then see if the result is a power of 2. If so, output it; it's a Mersenne prime.

If you can prove primality in time O(log^4 n) then this takes time O(x log^4 x) to find the Mersenne primes up to x. If you pretest with Miller-Rabin, the time drop to O(x log^3 x).

If you use Lucas-Lehmer, it takes time O(log^3 x log log log x).[/QUOTE]

I have a faster way using the 6(4x+1)+1 sequence I talked of earlier 24(1)+7 = 31

24(5)+7 = 127
24(21)+7 = 511

can we knock out a lot of the sequence through using comparison of 24n+7 intersecting the list made by (6n-/+1)*p ?

[QUOTE=science_man_88;223715] can we knock out a lot of the sequence through using comparison of 24n+7 intersecting the list made by (6n-/+1)*p ?[/QUOTE]

I don't know what you mean by that. It seems like a suggestion for some form of trial division, which would not be faster than the (very slow) method I proposed above.

[QUOTE=CRGreathouse;223725]I don't know what you mean by that. It seems like a suggestion for some form of trial division, which would not be faster than the (very slow) method I proposed above.[/QUOTE]

so starting with less and figuring a pattern to knock them out isn't going to be more efficient ?

[QUOTE=science_man_88;223740]so starting with less and figuring a pattern to knock them out isn't going to be more efficient ?[/QUOTE]

Your pattern is so dense that even if you could knock out one per nanosecond it would still be too slow.

[QUOTE=CRGreathouse;223747]Your pattern is so dense that even if you could knock out one per nanosecond it would still be too slow.[/QUOTE]

I'm talking knocking possible 1000's or more out with every pattern found.