After n=333,333, our next exponent will be...
 

Since we've just found a twin :grin:, 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.

[b]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.[/b]

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

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

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

[QUOTE=axn1;96258]If someone can post the typical FFT size (using LLR) for SSE2 & non-SSE2 machines, that'll probably help to make an informed decision.[/QUOTE]

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

[QUOTE=pacionet;96228]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).[/QUOTE]
OK, if you have enough computing power (at least 2 Athlons or 3 Intel's) and RAM (at least 1G).

[QUOTE]Can we decide the exponent as soon as possible ? (not a month, but some days ?)[/QUOTE]
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.

[QUOTE]
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[/QUOTE]
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 :smile:

I'll wait for what n you decide.

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?

a question or suggestion
 

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

[QUOTE=Cybertronic;96302]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 !)
[/QUOTE]

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.

[quote=Padanian;96299]It's been a long time since my days at school: does 2^2^19 simplifies in something else?[/quote]

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 ).