After n=333333, our next exponent will be... (revised poll)

[MooooMoo]

Since we've just found a twin , I made this poll to let people decide which n to sieve after n=333,333. The final votes will be counted by the end of the month, so there'll be enough time to sieve whichever n comes after n=333,333.

As a reference,

n= 400,000 takes about 2.07 times as much computing power to find a twin than n=333,333
n= 460,000 takes about 3.63 times as much computing power
n= 520,000 takes about 5.92 times as much computing power
n= 580,000 takes about 9.17 times as much computing power

Also, n=333,333 is expected to take 73 Pentium 4 (3.4 Ghz) CPU years before we find a twin.

edit: As usual, the votes are public because I'm only counting the votes of people who contributed to the project for n=195000. Of course, non-participants may express their opinions and suggest candidates.

important edit #2: I made a new poll because there was too much overlap. The most popular options (n=500K, n=2^19, n=587K, and n=number big enough for a 200000 digit prime) were all in the same category. This revised poll should fix the problem, but you'll need to vote again.

[R. Gerbicz]

My suggests, a little larger:
n=500,000
n=524,288 this is 2^19, nice number.

[pacionet]

MooMoooo I'd like to start sieving this exponent from scratch and provide regularly the pre-sieved files on twinprimesearch.org (given that soon all LLR testing will be done by PrimeGrid).

Can we decide the exponent as soon as possible ? (not a month, but some days ?)

Somebody has proposed this roadmap:

Goal : Digits : n : Remarks :
------- --------- ---------- ---------
1 58,710 195,000
2 100,000 332,190
3 175,258 582,192 > 500,000 exponent*
4 200,000 664,383
5 400,515 1,330,480 >1,000,000 exponent*
6 500,000 1,660,961
7 801,030 2,660,962 >2,000,000 exponent*
8 1,000,000 3,321,925
9 3,252,575 10,804,819 >5,000,000 exponent*
10 5,000,000 16,609,638


Thanks

[axn]

If someone can post the typical FFT size (using LLR) for SSE2 & non-SSE2 machines, that'll probably help to make an informed decision.

[Prime95]

Originally Posted by axn1

If someone can post the typical FFT size (using LLR) for SSE2 & non-SSE2 machines, that'll probably help to make an informed decision.

Be sure to choose a k value (in k*2^n+/-1) that is large - say 10 or 11 digits - when you do timings

[MooooMoo]

Originally Posted by pacionet

MooMoooo I'd like to start sieving this exponent from scratch and provide regularly the pre-sieved files on twinprimesearch.org (given that soon all LLR testing will be done by PrimeGrid).

OK, if you have enough computing power (at least 2 Athlons or 3 Intel's) and RAM (at least 1G).

Can we decide the exponent as soon as possible ? (not a month, but some days ?)

The new poll will close earlier, but it should give people enough time to make their decision. Any shorter time period won't give the people who are on vacation a chance to vote.

Somebody has proposed this roadmap:

Goal : Digits : n : Remarks :
------- --------- ---------- ---------
1 58,710 195,000
2 100,000 332,190
3 175,258 582,192 > 500,000 exponent*
4 200,000 664,383
5 400,515 1,330,480 >1,000,000 exponent*
6 500,000 1,660,961
7 801,030 2,660,962 >2,000,000 exponent*
8 1,000,000 3,321,925
9 3,252,575 10,804,819 >5,000,000 exponent*
10 5,000,000 16,609,638


Thanks

582,192 doesn't seem like a nice number. If you want one in that range, I'd prefer 585858, 585585, 580000, 555555, or 600000. 585000 is fine with me too, since it's exactly 3 times n=195000

[pacionet]

I'll wait for what n you decide.

[Padanian]

either n=400.000 or 444.444 or the largest prime <400.000

It's been a long time since my days at school: does 2^2^19 simplifies in something else?

[Cybertronic]

Why don't search the group for twins with form k*p#+/-1 ?
I know that a PRP-Test is 4 times slower,but :

- its possible we scan k's from 0 to 2000M with one task and we have one k for a 100k digit twin (to sieve 50G is a lot of time !)

- serveral people can uncase an the first that comes along interval and have perhaps a full strike in very short time.

best and thanks for comments

[R. Gerbicz]

Originally Posted by Cybertronic

Why don't search the group for twins with form k*p#+/-1 ?
I know that a PRP-Test is 4 times slower,but :

- its possible we scan k's from 0 to 2000M with one task and we have one k for a 100k digit twin (to sieve 50G is a lot of time !)

Yes, the PRP is much slower and the sieving is also much slower. For every q sieving prime you have to calculate (p#) mod q, and this is an expensive thing, O(p/log(p)) mulmod operations, but for k*2^n+-1 sieve it is only O(log(n)) mulmod, and this is (much) smaller.

And look at the top 20 twin primes all of them are in the form k*2^n+-1. This is the fastest way to find a twin prime.

[pschoefer]

Originally Posted by Padanian

It's been a long time since my days at school: does 2^2^19 simplifies in something else?

It's an "exponent tower", which you can't simplify. To calculate this number you have to calculate 2^19(=524.288) first, then you have to calculate 2^524.288(=No, I won't write it out:surprised ).