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2009-01-28, 19:10   #1
philmoore

"Phil"
Sep 2002
Tracktown, U.S.A.

3×373 Posts
Another record probable prime found!

Ben Maloney (paleseptember) reports:

Quote:
 Please find attached the results file for PRP 2.21-2.25M. I think you'll be interested in this line: [Mon Jan 26 01:09:36 2009] UID: paleseptember, 2^2249255+28433 is a probable prime! Wd1: B147D57F,00000000 Jan 26 is Australia Day down here. A fair present wouldn't you say?

A fair present indeed! Now that this entry has been verified by several strong probable prime tests, we can safely announce that Five or Bust has eliminated the second of its five troublesome sequences! Not only that, but 28433 was the toughest sequence of the five, with its elimination doing the most for improving our chances of eventually solving this problem. A new 3 k sieve file has been uploaded, and the latest work files also reflect the elimination of 28433. We reduced our PRP work by 16.1%. Now the percentage of remaining candidates in each sequence is as follows:

2131: 30.2%
40291: 34.8%
41693: 35.0%

The new updated probabilities for solving this problem with a search to a particular n value are as follows:

10%: all n < 2.5 x 10^7
50%: all n < 9.7 x 10^8
90%: all n < 9.1 x 10^11

If you compare these numbers with those cited in the paper, you will see how much the elimination of our low weight sequence has improved our chances.

How long would it take to prove this number prime? I estimate about 3 billion years, given our current level of theory and technology. Of course, if someone could prove the Generalized Riemann Hypothesis, we could prove it is prime using 3 billion computers in just 1 year.

At 677,094 digits, this number should appear soon as #1 on the Lifchitz web-page of largest known probable primes.

Congratulations, everyone, sievers and prp testers alike! A great achievement!

Last fiddled with by philmoore on 2009-02-16 at 22:58 Reason: changed 40293 to 40291

2009-01-28, 21:09   #2
engracio

May 2007

112 Posts

Quote:
 Originally Posted by engracio Congratulation Ben and Phil. Great job. Let's find another one.

e

 2009-01-28, 22:15 #3 paleseptember     Jun 2008 Wollongong, .au B716 Posts Ahem. I could not believe it! Tis pretty exciting :] I hope this generates some interest for the project, as those numbers that Phil quoted as truly scary! And huge credit to the hard-working sievers who make the PRP files so much shorter! Happy happy joy joy!
 2009-01-28, 23:41 #4 engracio     May 2007 11110012 Posts Happy happy joy joy! I like this, LET"S DO IT AGAIN.!!!!! Woohooooo ee
 2009-01-29, 00:19 #5 philmoore     "Phil" Sep 2002 Tracktown, U.S.A. 3·373 Posts I calculate that we should expect about 0.558 new primes for each doubling of the search range, i.e., 2.35 million to 4.7 million for example. I am optimistic that we will find the next one before too long, but the last one or two may require a bit of luck. Note that the low end estimate says that we have a 10% chance of solving this problem by searching the last sequence up to 7.5 million decimal digits, which sounds like a lot, but is definitely within the realm of possibility. Here is a new updated graphic. We aren't even close yet to 2^22, maybe we can pull that last point down!
 2009-01-29, 01:22 #6 Kman1293   Feb 2008 11 Posts Congratulations Ben and Phil! Three to go!
 2009-01-29, 13:31 #7 Cruelty     May 2005 23×7×29 Posts Congratulations!
 2009-01-29, 14:29 #8 Lennart     "Lennart" Jun 2007 112010 Posts Congratulations /Lennart
 2009-01-30, 01:22 #9 geoff     Mar 2003 New Zealand 13×89 Posts This is great news, to find a prime for the lightweight sequence early! Once we get down to two sequences it might be worthwhile sieving them separately. I will have to work on adding the dual mode to sr1sieve before Ben finds another PRP :-) Last fiddled with by geoff on 2009-01-30 at 01:22
2009-01-30, 01:53   #10
engracio

May 2007

112 Posts

Quote:
 Originally Posted by geoff This is great news, to find a prime for the lightweight sequence early! Once we get down to two sequences it might be worthwhile sieving them separately. I will have to work on adding the dual mode to sr1sieve before Ben finds another PRP :-)
With his luck he probably will. Go ahead Ben and reserve more prp files.

Woohoo

I like the waves, LET's DO IT AGAIN.!!!!!!!

 2009-01-30, 04:26 #11 paleseptember     Jun 2008 Wollongong, .au 18310 Posts One more set of waves? Yeah, why not I'm running the remaining +28433 tests from my reservations first to confirm that this actually is the smallest PRP for 28433. Do we have estimates, or ways to find estimates, on the expected improvement for sieving now that this sequence has been removed? Having really well-sieved work files is wonderful! Thanks(!) to you Geoff for making the sieving more and more efficient constantly! Every test saved is awesome

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