Archived sieve reservations and discussions

[mdettweiler]

Originally Posted by 10metreh

A "not" seems to have sneaked into your post.

Ah, right--thanks for catching that. I meant to say "not entirely unattainable".

[MooMoo2]

Originally Posted by mdettweiler

At this sieve depth (605T contiguous) and n- and k-level, the odds of finding a (non-twin) prime on a given candidate are 1 in 5490--that is, one would expect a prime about every 5490 candidates. The odds of finding one prime in the n=480071-480200 range currently loaded into the PRPnet server (4645 candidates) are about 57%. So it's a little better than a toss-up that there will be at least one prime found within the next few days at current processing rates.

There's already been a lot of LLRing going on. You have about 3050 tests from the manual reservations, 2212 from PRPnet, and another ~500 from LLRnet. That's over 5700 tests, and it doesn't include the ~10,000 tests done in the n=390,000 subproject. So TPS has gone primeless despite testing about 16,000 k/n pairs.

BTW, what are the chances of finding a twin in the 480000<n<485000 range for k<10M?

How many cores do you have? Oddball's got 6, but you can still crank out a decent amount of pairs (enough to likely get a prime within a couple of weeks) with 4 or even 2 cores. With 1 core it would take a bit longer, but a prime is still not attainable.

I'm putting 1-2 cores on this project (the rest of my cores are working on an individual k reservation).

Note that despite all my above words to encourage you that finding a prime isn't really impossible , it actually is better in the long run to sieve instead at this time. We're still quite a ways from optimal depth at p=6P, so running LLR tests right now is not really the most efficient way to go. (It's more to break the monotony of sieving than anything else. )

At p=6P, what are the odds that a k/n pair would be prime? Would it be much better than the 1 in 5490 odds of finding a prime at today's depth of p=605T? Just wondering.

[mdettweiler]

Originally Posted by MooMoo2

There's already been a lot of LLRing going on. You have about 3050 tests from the manual reservations, 2212 from PRPnet, and another ~500 from LLRnet. That's over 5700 tests, and it doesn't include the ~10,000 tests done in the n=390,000 subproject. So TPS has gone primeless despite testing about 16,000 k/n pairs.

Note that when I say we'd expect a prime every 5490 candidates, that actually means that after testing exactly 5490 candidates, there is a ~62% chance that a prime will have been found. (Why this is involves some more advanced probability math which I myself don't entirely understand; I picked up most of this stuff from Gary at the NPLB project who is our resident probability whiz.) So having tested ~5700 tests so far on the variable-n drive, there's a 64% chance that we'll have found a prime so far--or, a 36% chance that we won't have found a prime yet. Thus, what we have observed is an event that is statistically predicted to happen 36% of the time--which is well within the realm of possibility.

Informally, I could say that we are "due" for a prime at this point. But that's techincally an expression of the "gambler's fallacy" since having not found a prime so far does not have any bearing on whether we will find one soon (because they are independent events). More precisely, I could say that I'd expect to find a prime some time soon because as we test more pairs, it becomes less and less statistically likely that we won't have found a prime.

BTW, what are the chances of finding a twin in the 480000<n<485000 range for k<10M?

For the entire n=480K-485K, k<10M range we would expect:
-3264.835 single primes
-0.592 twins

Put otherwise, there's a ~45% chance that we'll find a twin in this range. Multiplying that by 4 for the entire n=480K-500K range, we get a ~90% chance of finding a twin.

I'm putting 1-2 cores on this project (the rest of my cores are working on an individual k reservation).

In that case, then, a prime should be quite reasonably attainable. I would expect two cores running 24/7 on LLRing to find a (non-twin) prime within a couple of weeks. (Very rough estimate, though it should be approximately correct.) Note, of course, that one can always "beat the odds" and still not find a prime after that long.

At p=6P, what are the odds that a k/n pair would be prime? Would it be much better than the 1 in 5490 odds of finding a prime at today's depth of p=605T? Just wondering.

The odds that a particular k/n pair will be prime do not change with sieve depth. However, what does change is that a lot of the pairs are eliminated during sieving, so it doesn't take as long to search the same range.

[MooMoo2]

Originally Posted by mdettweiler

Note that when I say we'd expect a prime every 5490 candidates, that actually means that after testing exactly 5490 candidates, there is a ~62% chance that a prime will have been found. (Why this is involves some more advanced probability math which I myself don't entirely understand; I picked up most of this stuff from Gary at the NPLB project who is our resident probability whiz.) So having tested ~5700 tests so far on the variable-n drive, there's a 64% chance that we'll have found a prime so far--or, a 36% chance that we won't have found a prime yet. Thus, what we have observed is an event that is statistically predicted to happen 36% of the time--which is well within the realm of possibility.
...
For the entire n=480K-485K, k<10M range we would expect:
-3264.835 single primes
-0.592 twins

Put otherwise, there's a ~45% chance that we'll find a twin in this range. Multiplying that by 4 for the entire n=480K-500K range, we get a ~90% chance of finding a twin.

I see. Thanks for the explanation.

Oddball, you can move this discussion to a seperate thread if you want.

[Oddball]

PRPnet and LLRnet are both down, so I'll take 720T-730T.

[mdettweiler]

710T-715T complete, 7482 factors: http://www.sendspace.com/file/4frdyp

Reserving 730T-735T.

[Lennart]

Reserving 735T-740T. Lennart I will test this on CUDA. Only a slow 250 card.

[gribozavr]

605T-700T complete. Taking 740T-900T.

[MooMoo2]

715T-720T complete, 7288 factors found:

http://www.sendspace.com/file/bs64ce

[Lennart]

http://pgllr.mine.nu/privat/local/tps_735T-740T.txt

735T-740T complete


Lennart

[Oddball]

720T-730T complete, about 14500 factors found:

http://www.sendspace.com/file/cayaop