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Old 2007-01-16, 03:39   #56
jinydu
 
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Quote:
Originally Posted by Flatlander View Post
The other one's bigger!
I presume you mean 2^{32582657}-1

Quote:
Originally Posted by Flatlander View Post
Maybe Perfectly Scientific Inc. will make a pair of posters.
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.

Last fiddled with by jinydu on 2007-01-16 at 03:42
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Old 2007-01-16, 04:35   #57
MooooMoo
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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?
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Old 2007-01-16, 05:12   #58
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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 PARI/GP
Code:
p=2003663613*2^195000-1; write("p58711.txt",p);
Attached Files
File Type: pdf p58711.pdf (51.0 KB, 191 views)

Last fiddled with by Kosmaj on 2007-01-16 at 05:14
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Old 2007-01-16, 07:03   #59
Rytis
 
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I can notify automatically. How?
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Old 2007-01-16, 08:56   #60
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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) ?
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Old 2007-01-16, 09:42   #61
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Maybe you can send a brief announcement to the NMBRTHRY list.

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

Alex

Last fiddled with by akruppa on 2007-01-16 at 09:43
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Old 2007-01-16, 12:59   #62
Xyzzy
 
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This needs updated:

http://www.mersennewiki.org/index.php/Twin_primes
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Old 2007-01-16, 14:08   #63
Flatlander
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Quote:
Originally Posted by jinydu View Post
I presume you mean 2^{32582657}-1
No, I meant the other twin.

Quote:
Originally Posted by jinydu View Post
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.
That was a joke too. Either side of the fireplace would look nice.
Maybe I should use more smilies, I'm soooo misunderstood.
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Old 2007-01-16, 16:51   #64
MooooMoo
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Quote:
Originally Posted by pacionet View Post
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) ?
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%

Last fiddled with by MooooMoo on 2007-01-16 at 17:04 Reason: more stats :)
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Old 2007-01-16, 23:40   #65
ATH
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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
.
.
.

What is the formula for these probabilities for different n's?
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Old 2007-01-17, 01:14   #66
R. Gerbicz
 
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Quote:
Originally Posted by ATH View Post
What is the formula for these probabilities for different n's?
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)))

Last fiddled with by R. Gerbicz on 2007-01-17 at 01:16
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