How important is memory bandwidth for P-1, particularly for very large exponents?

I don't suppose someone could try P-1 using four or more SSD's in Raid 0?

[QUOTE=lbh134679;352301]A factor of MM61 and MM127 can be found, I guess, above 10^100 or even 10^1000. Well, probably.[/QUOTE]

And on what basis do you make such a claim?

[QUOTE=TheMawn;352356]How important is memory bandwidth for P-1, particularly for very large exponents?

I don't suppose someone could try P-1 using four or more SSD's in Raid 0?[/QUOTE]

Lol, wouldn't that completely kill your SSDs?

[QUOTE=Prime95;352358]And on what basis do you make such a claim?[/QUOTE]
For P>127 and 2^P-1 is prime (like 521,607,1279……57885161), none of the Ps can be expressed as 2^N-1, 2^N+1, 4^N-3, or 4^N+3. But it is not a theory, so I put "I guess", MM61 and MM127 are both composite, perhaps their smallest factors are extremely big.

[QUOTE=lbh134679;352367]...But it is not a theory...[/QUOTE]
Correct.
[QUOTE=lbh134679;352367]... perhaps their smallest factors are extremely big.[/QUOTE]
Define "extremely big".

The first rule of math club is -- you forget all the colloquial meanings of words.
The second rule of math club is -- you forget all the colloquial meanings of words.
The third rule of math club is -- you define the meaning of all new words that you create, unless they are in the established vocabulary (which is a learnable skill).
The forth and last rule of math club is -- if this is you first night at the club, you have to fight. (or else - you can lurk and listen... or you add a question mark to anything you utter.)

:smile: ...take it easy!

[QUOTE=Batalov;352370]The forth and last rule of math club is -- if this is you first night at the club, you have to fight. (or else - you can lurk and listen... [B]or you add a question mark to anything you utter[/B].)[/QUOTE]

LMFAO!!!!!

There's [URL="https://class.coursera.org/thinkagain-002/class"]a very likable Coursera class[/URL] on right now, so I guess some of the terminology simply rubs in. You see, the professor makes a clear distinction there - between utterances, linguistic acts, speech acts, and finally arguments. (and that's is even before the discussion of strength and validity an arguments. That is some utterances are not linguistic acts, not all linguistic acts are speech acts, and not all of those are even entering arguments. It's loads of fun! I recommend joining if it is still open.)

[QUOTE=Batalov;352370]Correct.

Define "extremely big".

The first rule of math club is -- you forget all the colloquial meanings of words.
The second rule of math club is -- you forget all the colloquial meanings of words.
The third rule of math club is -- you define the meaning of all new words that you create, unless they are in the established vocabulary (which is a learnable skill).
The forth and last rule of math club is -- if this is you first night at the club, you have to fight. (or else - you can lurk and listen... or you add a question mark to anything you utter.)

:smile: ...take it easy![/QUOTE]
Maybe I should use "very high". Catalan's Mersenne Conjecture is likely to be an example of the Strong Law of Small Numbers. However, once MM127 is proved to be prime, the Conjecture may remain unsolved forever, for MMM127 is much too high to test. Unless the Conjecture is proved.

In post 15, you labelled MM127 composite. In Post 19, you say "once MM127 is proved prime". Which side of this is your non-theory utterance positing is true, and why?

How does using "very high" help you to communicate how high you mean, or how much a GPU will help you get there?

[QUOTE=VBCurtis;352385]In post 15, you labelled MM127 composite. In Post 19, you say "once MM127 is proved prime". Which side of this is your non-theory utterance positing is true, and why?

How does using "very high" help you to communicate how high you mean, or how much a GPU will help you get there?[/QUOTE]
No one knows whether MM127 is prime right now, but I hope it is composite, because it is helpful for us to solve the problem of "Catalan Mersenne Conjecture".
The best way to prove MM127 is composite is to find a factor. What we could do is to search for it, no matter how high it is.:smile:

[QUOTE=lbh134679;352388]
The best way to prove MM127 is composite is to find a factor. What we could do is to search for it, no matter how high it is.:smile:[/QUOTE]

So far, MM127 has had trial division done from k=1 to k=72,500,000,000,000,000 with no factor found, except for the range from k=33,500,000,000,000,000 to k=35,000,000,000,000,000. k=72,500,000,000,000,000 is about 184 bits. People are already trying to factor it at very high bounds, and it only gets more and more time-consuming to continue each higher bit level.