Will Any Current 100M Digit LL Tests Finish?

[davieddy]

Originally Posted by jinydu

I've never seen M(number) being used to refer to number of decimal digits.

No and he didn't say it was.

[Uncwilly]

Originally Posted by retina

M_43112609 = M46

I would vote for M(43112609) = M46

[davieddy]

Originally Posted by retina

Perhaps we could have some form of forum convention.

M_{[I]number[/I]} refers to: number = exponent

Mnumber refers to: number = number^th mersenne prime

eg.

M_43112609 = M46

Isn't there already a convention that M(n) = 2^n - 1 ?
It's easier to type than a subscript.

[davieddy]

Originally Posted by Uncwilly

I would vote for M(43112609) = M46

Snap (crosspost)

[retina]

Sure, okay, brackets also. Fine by me just as long as everyone knows and uses it.

But somehow I get the feeling that we will still see the likes of M8191, changing the world is so hard :(

[davieddy]

It's pretty ubiqitous on this forum to say "exponent" when that is what we
mean. One might equally well say bits.
"Digits" by default means decimal digits.
Using M29 to denote the 29th Mersenne prime has become
ingrained around here.

[starrynte]

Is the nth Mersenne prime the nth discovered, or the nth largest? (I'm assuming the nth largest, but just to make sure...)

[davieddy]

Originally Posted by starrynte

Is the nth Mersenne prime the nth discovered, or the nth largest? (I'm assuming the nth largest, but just to make sure...)

Yes. nth largest.

[dmoran]

I just checked using a Core i7 920 and it shows well under 5 years.


[Jan 6 14:38] Setting affinity to run helper thread 1 on logical CPU #1
[Jan 6 14:38] Setting affinity to run helper thread 2 on logical CPU #2
[Jan 6 14:38] Setting affinity to run helper thread 3 on logical CPU #3
[Jan 6 14:38] Using FFT length 20M, 4 threads
[Jan 6 14:38] p: 332190991. Time: 127.856 ms.
[Jan 6 14:38] p: 332190991. Time: 130.867 ms.
[Jan 6 14:38] p: 332190991. Time: 130.332 ms.
[Jan 6 14:38] p: 332190991. Time: 130.673 ms.
[Jan 6 14:38] p: 332190991. Time: 130.613 ms.
[Jan 6 14:38] Iterations: 5. Total time: 0.650 sec.
[Jan 6 14:38] Estimated time to complete this exponent: 500 days, 2 hours, 4 minutes.

[jinydu]

Impressive. And the Core i7 940 could probably finish even faster.

[lfm]

Originally Posted by jinydu

[Detour]

Here is the continuous version of the problem.

Suppose that you have a limited budget (1 unit of money) and want to finish an LL test (1 unit of computing work) at the earliest time possible. At each instant of time, one can buy a computer; the computer's speed is proportional to the amount of money one spends. However, because of continual improvements in technology, the constant of proportionality decays exponentially with time. Treating money as a continuous variable, what is the optimum way to distribute the budget?

...

[/Detour]

in the real world you can get a 3 year old computer free! I know cuz some of my gimps machines are such! I guess you still have costs of electricity but thats pretty cheap really too. It would mean that if the job is big enuf that your calculation indicates you shouldnt buy any machine for a while yet, you can still start the calculation on free hardware and upgrade it frequently till you decide to spend money on the project.