Assumptions: m, t, p, n are positive integers, p > 1.

[QUOTE=science_man_88;225054][TEX]24m= 6tp+(p-7)\right m=px+c [/TEX]
[TEX] 24m=6tp-(p+7)\right m=px+c ? [/TEX][/QUOTE]

So we have 24m + 7 being an integer with [TEX]24m+7=p(6t\pm1)[/TEX] as appropriate.

[QUOTE=science_man_88;225054][TEX]if(px+c==(4^n-1)/3,(4^\strike n -1)/3[/TEX][/QUOTE]

So if m is of the form (4^n-1)/3, you're saying that 2n+3 is not a Mersenne exponent. That is, if 24 * (4^n-1)/3 + 7 is composite, 2n+3 is not a Mersenne exponent. That is, if 8 * (2^(2n) - 1) + 7 is composite, 2n+3 is not a Mersenne exponent. That is, if 2^(2n+3) - 1 is a composite, 2n+3 is not a Mersenne exponent.

[QUOTE=CRGreathouse;225074]Assumptions: m, t, p, n are positive integers, p > 1.



So we have 24m + 7 being an integer with [TEX]24m+7=p(6t\pm1)[/TEX] as appropriate.



So if m is of the form (4^n-1)/3, you're saying that 2n+3 is not a Mersenne exponent. That is, if 24 * (4^n-1)/3 + 7 is composite, 2n+3 is not a Mersenne exponent. That is, if 8 * (2^(2n) - 1) + 7 is composite, 2n+3 is not a Mersenne exponent. That is, if 2^(2n+3) - 1 is a composite, 2n+3 is not a Mersenne exponent.[/QUOTE]


something tells me you are getting at a trivial answer ?

[QUOTE=CRGreathouse]What script are you using to check? My isSPRP gives
[/QUOTE]

Nono, it's not PARI. It's a separate application. It's supposed to be an implementation of the Miller-Rabin primality test. I in fact used PARI to verify that it was indeed an error.

[QUOTE=CRGreathouse]So if m is of the form (4^n-1)/3, you're saying that 2n+3 is not a Mersenne exponent. That is, if 24 * (4^n-1)/3 + 7 is composite, 2n+3 is not a Mersenne exponent. That is, if 8 * (2^(2n) - 1) + 7 is composite, 2n+3 is not a Mersenne exponent. That is, if 2^(2n+3) - 1 is a composite, 2n+3 is not a Mersenne exponent.
[/QUOTE]

Those are all trivially correct. There is no grand discovery here.

[QUOTE=3.14159;225082]Those are all trivially correct. There is no grand discovery here.[/QUOTE]

The difficult discovery that I made was determining sm88's method. Once that was accomplished, it was not hard to determine that the method came down to "Mersenne numbers are prime iff they are prime".

[QUOTE=3.14159;225081]Nono, it's not PARI. It's a separate application. It's supposed to be an implementation of the Miller-Rabin primality test. I in fact used PARI to verify that it was indeed an error.[/QUOTE]

Really? Interesting.

[QUOTE=CRGreathouse;225074]That is, if 2^(2n+3) - 1 is a composite, 2n+3 is not a Mersenne exponent.[/QUOTE]

But this is the other way round: M(n)=2^n-1 can be prime, so n must be a prime!

[QUOTE=CRGreathouse]The difficult discovery that I made was determining sm88's method. Once that was accomplished, it was not hard to determine that the method came down to "Mersenne numbers are prime iff they are prime".
[/QUOTE]

Wow. That was all that it was? A tautology/circular argument? :lol:!

[QUOTE=CRGreathouse]Really? Interesting.
[/QUOTE]

You can get it for yourself [URL="http://www.naturalnumbers.org/"]here[/URL].

I suspect it of being a kook site, but, seeing as their applets work correctly to some extent, I am undecided on that matter.

Try testing it out quickly (Note: Small integers only, please), and if you can catch 25326001 as an error, please note it!

[QUOTE=kar_bon]But this is the other way round: M(n)=2^n-1 can be prime, so n must be a prime!
[/QUOTE]

Karsten, I found that you were right about the differences in testing times based on the k-values used.

[QUOTE=kar_bon;225085]But this is the other way round: M(n)=2^n-1 can be prime, so n must be a prime![/QUOTE]

The claim (once all the window-dressing was removed) was that if 2^n - 1 is prime, then 2^n - 1 is prime.

Or rather, it was a restricted case of this: if n > 3 is an odd number such that 2^n - 1 is prime, then 2^n - 1 is prime.

[QUOTE=CRGreathouse]The claim (once all the window-dressing was removed) was that if 2^n - 1 is prime, then 2^n - 1 is prime.
[/QUOTE]

Call the press! We're going to be filthy rich!

Amirite?

[SPOILER]Bullshit aside.. [/SPOILER]

CRG, have you managed to do some testing on 25326001 using that app? Does it say that it's a 7-SPRP?