20091123, 17:30  #1  
"Phil"
Sep 2002
Tracktown, U.S.A.
1119_{10} Posts 
Fourth probable prime found, one to go!
Engracio sent this in last Tuesday:
Quote:
I want to note that this is an incredibly lucky discovery! I estimated about a 6% chance of finding another probable prime between the exponent of the previous one, 4583176 and this one, 5146295. I was so surprised when Engracio reported it, but there it is, we can't argue with success! New work files and a new sieve file have been uploaded, now 40291 is the last odd k value < 78557 for which no prime or probable prime of the form 2^{n}+k is known. We eliminated 50.2% of our prp tests, and we now can expect about 0.19166 probable primes in any interval where our exponents double, for example, in the range from n=5.15M to n=10.30M. So we could solve this problem tomorrow, or it could take us a long time! I haven't computed the probabilities yet, but I am sure they have come down, now that we have only one left to find. But the show ain't over till the fat prime sings! The probability that a random number of this size would be composite after having passed all of these strong probable prime (MillerRabin) tests is < 10^{1360}. I estimate that it would take around 225 billion years to prove it is prime if we could gear up ECCP on a single process, maybe only 60 billion years or so if the generalized Riemann hypothesis were proven. Hopefully, someone will come up with better primality proving algorithms before then. Here is a graph comparing the progress between this problem and the Sierpinski problem. Note how much the last point has dropped. Dropping like a stone, hopefully... Let's go find that last probable prime! Last fiddled with by philmoore on 20091124 at 04:45 Reason: minor typo 

20091123, 17:48  #2 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17·251 Posts 
Someone besides paleseptember found one of 'em, for once! The obligatory: I think we should now expect to have to search to 63.17M (63.17M=5.15M*2^(X/.19166) with X such that e^(X)=0.5) to get a 50% chance of a prime. How lousy. Hopefully the odds are beaten. On the other hand, there's a decent chance this project could find the first 10M+ digit PRP. We shouldn't expect 1 prime until 191.63M. The odds of at least one by then is only about 63.21%. Last fiddled with by MiniGeek on 20091123 at 18:06 
20091123, 18:41  #3  
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
3×1,951 Posts 
Quote:
on this project the predictions keep on being way too high for instance 

20091123, 19:08  #4 
May 2007
11^{2} Posts 
version 4.0.1
What no ??? Come on guys let's Wohoooooo 
20091123, 19:13  #5 
Jan 2007
Germany
13×23 Posts 
Congratulation to your FoB team !!!
Norman 
20091123, 22:45  #6 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
5·1,877 Posts 
Wow!

20091123, 22:58  #7 
Jun 2008
Wollongong, .au
3·61 Posts 
I believe these are in order? Excellent news, fantastic effort for all involved, including the sievers too! They make life so much easier for the PRPtesters. Oh, and I love the new look workfiles ;] So much more compact! 
20091123, 23:39  #8 
"Phil"
Sep 2002
Tracktown, U.S.A.
3·373 Posts 
Thanks to (alphabetically) Ben, Dmitry, Engracio, Geoff, Greg, Hadrian, Jayson, Jeff, Karsten, Kent, Lennart, Max, Phil, Serge, Tim, Winnie, and Yves, all of whom have contributed time either prp testing, sieving, or both.
Thanks also to George Woltman for the prp testing software, to Geoff Reynolds for the sieving software, and to Mike Vang (xyzzy) for hosting a home for us. And now, the odds: 10% chance of finishing by 7.5x10^{6} 50% chance of finishing by 6.3x10^{7} 90% chance of finishing by 2.1x10^{10} Compare this to http://www.mersenneforum.org/showthread.php?t=12376 to see that our odds have dramatically improved. I don't see any reason that the odds can't improve even more! 
20091124, 00:14  #9 
May 2007
11^{2} Posts 
Phil,
I'd like to know how you feel about his one question. Since we are on the last sequence, how do feel about immediately posting a possible prime candidate for the last sequence so that we/others can immediately start other dc project while awaiting confirmation? In the unlikely event that it is a false positive, the temp stoppage would be a day or so at most. 
20091124, 00:43  #10  
"Phil"
Sep 2002
Tracktown, U.S.A.
3×373 Posts 
Quote:
http://www.research.att.com/~njas/se...nguage=english But if anyone wants to jettison the rest of their tests next time, no problem, I am willing to finish them. The work stoppage may be more than a day or two if the next prp is quite a bit larger, but the prospect of a false pseudoprime is pretty remote. Of course, this assumes that the project stays small. If it grows a great deal, it would probably make more sense to do as you suggest. 

20091124, 01:14  #11 
Jun 2003
Ottawa, Canada
494_{16} Posts 
Congrats everyone, great work!
Now I'm starting to wonder if paleseptember = engracio as a second account because how is it possible for anyone besides him to find a PRP in this project?!?!?! Just kidding of course, looks like I just missed that reservation. Maybe next time. 
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