extending PrimeNet to the 10B range?

[ixfd64]

Currently, the PrimeNet database goes up to 1B. Would it be too early to extend the range up to 10B? This won't help a lot right now in terms of finding new Mersenne primes, but it could help groups like Operation Billion Digits coordinate their efforts.

[NBtarheel_33]

See here: http://www.mersenneforum.org/showthread.php?t=14089.

The consensus (or what there was of a consensus) was that extending even to 4 billion (which would include the smallest of the OBD exponents) is probably premature at this point.

The OBDers keep good enough records that it will be fairly simple to merge everyone's databases together in the years to come.

There might also be a waste of resources if we were to do this - no numbers of this size are likely to have an LL test this century, and P-1 would be similarly out of the question (Prime95 isn't even capable of handling these numbers for TF). So the most you could do is early TF, but then that might drag away computers from the more immediate goal of GIMPS: searching for Mersenne primes in ranges where LL tests are computationally feasible.

[Mr. P-1]

Originally Posted by NBtarheel_33

See here: http://www.mersenneforum.org/showthread.php?t=14089.no numbers of this size are likely to have an LL test this century,

There is a single hundred-milllion digit LL test recorded in the database. Moore's law would suggest that the first billion digit LL test will be done a few years from now.

But I agree that it will be decades before testing in this range becomes generally feasible.

[NBtarheel_33]

Originally Posted by Mr. P-1

There is a single hundred-milllion digit LL test recorded in the database.

Note that this test was affected by numerous likely fatal errors. I'll declare success on the 100Md front when we see a test come in with a 00000000 error code.

xorbe's test, of course, is still a milestone for GIMPS (he was, after all, the first to try such a test), but we still can't be confident that such large tests can be run on standard PC hardware without ECC memory, etc. etc.

Originally Posted by Mr. P-1

Moore's law would suggest that the first billion digit LL test will be done a few years from now.

According to Luigi's site (http://www.moregimps.it/billion/index.php), a billion-digit test started now on current hardware would take 850 years or so to complete. Let's say Moore cuts that in half every 1.5 years. It would take 9 years just to get in a timeframe where a single LL test could be done within one tester's lifespan (53.125 years). It takes 18 years to get the testing time under one year. And this, of course, (1) assumes that Moore's Law continues to hold (which indeed it may not for everyday PCs - does the average user need/want 128 cores?), (2) excludes any needed P-1 or TF work (P-1 alone is likely to take years at the present time), and (3) assumes that the result of this megatest is error-free! Oh yeah, and (4) don't forget the doublecheck!

Bottom line is that it's likely that we will not see a billion-digit test completed, error-free, for at least another 20-25 years, and probably more like 30-40. (So, maybe "not this century" was too pessimistic...)

Originally Posted by Mr. P-1

But I agree that it will be decades before testing in this range becomes generally feasible.

Well, if we consider that the LL wavefront is advancing by about 4M/year, it will be about 70 years before GIMPS hands out 100Md tests as normal, everyday assignments...and 800+ years before GIMPS hands out the billion digit tests! (Pardon my quasi-illiteration, but some views of eschatology eschew the availability of such time frames...on this planet in its current form, anyway. (I don't know what *scat*ology has to say but I suspect it would smell a bit off...))

[Mr. P-1]

Originally Posted by NBtarheel_33

According to Luigi's site (http://www.moregimps.it/billion/index.php), a billion-digit test started now on current hardware would take 850 years or so to complete.

Assuming Xorbe started his LL on the day he turned in its final TF, It took him a year and 3 months. The cost of an LL is O(N^2 log (N)) which suggests that a billion digit exponent would take about 290 years on the hardware he used.

Let's say Moore cuts that in half every 1.5 years. It would take 9 years just to get in a timeframe where a single LL test could be done within one tester's lifespan (53.125 years). It takes 18 years to get the testing time under one year.

Assuming Moore cuts that in half every 1.5 years, Xorbe should be able to start his billion digit LL exactly twelve years after he started his 100M, and complete it in less time.

And this, of course, (1) assumes that Moore's Law continues to hold (which indeed it may not for everyday PCs - does the average user need/want 128 cores?),

640K should be enough for anyone.

(2) excludes any needed P-1 or TF work (P-1 alone is likely to take years at the present time),

I would assume that he would start his P-1 and TF work a couple of months before starting his LL, as he did his 100M, and complete them on his 256 X faster machine in about the same time.

and (3) assumes that the result of this megatest is error-free! Oh yeah, and (4) don't forget the doublecheck!

You said nothing about the test being doublechecked and error-free, only that an LL would not be completed this century.

Bottom line is that it's likely that we will not see a billion-digit test completed, error-free, for at least another 20-25 years, and probably more like 30-40. (So, maybe "not this century" was too pessimistic...)

I expect we will see doublechecked, error-free 100M tests within the next couple of years. My prediction is that we will see a doublechecked error-free 100M test twelve years later.

Well, if we consider that the LL wavefront is advancing by about 4M/year, it will be about 70 years before GIMPS hands out 100Md tests as normal, everyday assignments...and 800+ years before GIMPS hands out the billion digit tests!

GIMPS is already handing out 100M digit assignments to anyone who wants one. The wavefront is a quite different metric. I make no predictions about that.

[cheesehead]

Originally Posted by Mr. P-1

640K should be enough for anyone.

Indeed, with each of those 640K CPUs running at a conservative 2.4 GHz (to ease cooling), that's over a petahertz-and-a-half one-and-a-half petahertz.

I expect we will see doublechecked, error-free 100M tests within the next couple of years. My prediction is that we will see a doublechecked error-free 100M test twelve years later.

I presume the latter was intended to be, "... we will see a doublechecked error-free 1B test twelve years later."