Another record probable prime found!

philmoore · 2009-01-28, 19:10

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!

engracio · 2009-01-28, 21:09

Quote:

Originally Posted by engracio

Congratulation Ben and Phil.

Great job.

Let's find another one.

e

paleseptember · 2009-01-28, 22:15

Ahem.

<Happy Dance>

</Happy Dance>

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!

engracio · 2009-01-28, 23:41

Happy happy joy joy!

I like this, LET"S DO IT AGAIN.!!!!!

Woohooooo

ee

philmoore · 2009-01-29, 00:19

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!

Click image for larger version

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Kman1293 · 2009-01-29, 01:22

Congratulations Ben and Phil!

Three to go!

Cruelty · 2009-01-29, 13:31

Congratulations!

Lennart · 2009-01-29, 14:29

Congratulations

/Lennart

geoff · 2009-01-30, 01:22

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 :-)

engracio · 2009-01-30, 01:53

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.!!!!!!!

paleseptember · 2009-01-30, 04:26

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 <grins>

2009-01-30, 01:22	#9
geoff Mar 2003 New Zealand 485₁₆ 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

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2009-01-28, 22:15	#3
paleseptember Jun 2008 Wollongong, .au 10110111₂ Posts	Ahem. <Happy Dance> </Happy Dance> 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 171₈ 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. 19×59 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 2²·11·37 Posts	Congratulations!

2009-01-29, 14:29	#8
Lennart "Lennart" Jun 2007 2⁵·5·7 Posts	Congratulations /Lennart

2009-01-30, 04:26	#11
paleseptember Jun 2008 Wollongong, .au 3×61 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 <grins>