[QUOTE=Flatlander;96259]The other one's bigger![/QUOTE]

I presume you mean [tex]2^{32582657}-1[/tex]

[QUOTE=Flatlander;96259]Maybe Perfectly Scientific Inc. will make a pair of posters. :smile:[/QUOTE]

If you're capable of making a poster with 9,808,358 digits, then 58,711 digits is utterly trivial. They could even print both twins on the same poster.

I emailed Chris Caldwell about the discovery and requested the project codes for TPS and PrimeGrid.

Rytis:

For the next n, our primes will be big enough to get into the top 5000 primes list. Will PrimeGrid submit those primes automatically, or will the finders have to submit their primes manually onto the site?

Here is one version of the poster on 2 pages in A3 format, in 8pt Ariel Narrow. It fits nicely. After the print out, cut the top margin on page 2 and paste it at the bottom of page 1. All margins are 12mm (1/2 inch) and can be printed on any A3 printer.

BTW, digits can be produced effortlessly using [URL="http://pari.math.u-bordeaux.fr/"]PARI/GP[/URL]
[CODE]
p=2003663613*2^195000-1; write("p58711.txt",p);
[/CODE]

I can notify automatically. How?

MoooMoo, or anyobdy else, if you have time, could you write a small paper (1 or 2 pages) describing our project and our discovery, putting some data in it (how many users, how many primes found before twins, probability, etc) ?

Maybe you can send a brief announcement to the NMBRTHRY list.

But in any case: Congratulations to the discoverers and all project participants! :banana:

Alex

This needs updated:

[url]http://www.mersennewiki.org/index.php/Twin_primes[/url]

[quote=jinydu;96260]I presume you mean [tex]2^{32582657}-1[/tex][/quote]

No, I meant the other twin.

[quote=jinydu;96260] If you're capable of making a poster with 9,808,358 digits, then 58,711 digits is utterly trivial. They could even print both twins on the same poster.[/quote]

That was a joke too. Either side of the fireplace would look nice.
Maybe I should use more smilies, I'm soooo misunderstood.

[QUOTE=pacionet;96287]MoooMoo, or anyobdy else, if you have time, could you write a small paper (1 or 2 pages) describing our project and our discovery, putting some data in it (how many users, how many primes found before twins, probability, etc) ?[/QUOTE]
I put a brief description of our project in my (late) official press release a few posts ago. Here are the project's stats (PrimeGrid and TPS combined):

- Number of users: 287
- Number of users who tested at least 1M: 129
- Number of users who found at least 1 prime: 91
- Number of non-twin primes found: 502
- Number of primes found by PrimeGrid: 304
- Number of primes found by TPS: 198
- Number of ranges complete: 1176M by TPS, 1620M by PrimeGrid, 2796M total
- Number of candidates tested: 1,006,560
- Average prime density: 1 prime every 5.57M
- Total amount of computing power: 315 P-90 CPU years (or 3.03 Pentium 4 CPU years (3.4 GHz))
- Days needed to find a twin: 277
- Time needed to find a twin: 9 months and 2 days
- Average prime discovery rate: 1.81 primes per day
- Average range completion rate: 10.09M per day
- Progress towards completing the whole 25G range: 11.18%
- Probability that a twin would be discovered after searching only 2796M: 22.1%

Gratz on the great discovery!



[QUOTE]Here it is a table for n=333333 (testing only odd k values):

Code:
k=5 G chance of finding a twin: 0.1163231920391812909933055240
k=10 G chance of finding a twin: 0.2191152990721783323150315761
k=15 G chance of finding a twin: 0.3099503000986639810061836904
.
.
.
[/QUOTE]


What is the formula for these probabilities for different n's?

[QUOTE=ATH;96346]What is the formula for these probabilities for different n's?[/QUOTE]

I've used twin prime conjecture to estimate what is the probability that a large random b,b+2 is a twin prime. Here it is the fast PARI program:
[CODE]
T=4.0;forprime(p=3,10^5,T*=(p-2)/p/(1-1/p)^2);p=T*(333333*log(2))^-2;\
forstep(i=5,100,5,print("k=",i," G ","chance of finding a twin:",\
1-(1-p)^(i*10^9/2)))
[/CODE]