Record probable prime found!

philmoore · 2009-01-07, 19:16

Congratulations to Ben Maloney (paleseptember) who discovered the probable prime $2^{1518191}+75353$ . At 457,022 decimal digits, it should soon appear as the new probable prime record at the website of Henri and Renaud Lifchitz, PRP Records, Probable Primes Top 10000. We have performed strong probable prime tests on this number to all 20 prime bases from 2 to 71. The probability that a random number of this size that passes even one strong probable prime test is composite is less than $10^{-728}$ . This eliminates the first of the five sequences, and should speed up our PRP testing by over 20% as well as our sieving by around 10%. I have already uploaded new work files and will get a new sieve file up soon as well. Thanks to everyone who contributed to this effort!

And now for the embarrassing part - this prp actually showed up in early November, but was not noticed by either of us! In fact, PRP testing is currently approaching 630,000 digits, a good bit beyond this record. I visually scanned all of the results files when they came in, but obviously, out of the more than 300 results in this file, I overlooked the important one! Moral: computers make fewer mistakes than humans, so always search the file for the string "probable". Ben says he did search, but specified the wrong string. Unfortunately, it means that 20% of our PRP testing the past two months was unnecessary, but in the long run, that is probably a drop in the bucket compared to what comes next. All I can say is that it will not happen again!

We are close to finishing PRP testing up to n=2^21, about 2.1 million. In the range from 2^21 to 2^22, I calculate that we should expect about 0.667 new primes. Let's go find another one!

engracio · 2009-01-07, 19:23

Congratulation Ben and Phil.

Great job.

Let's find another one.

TimSorbet · 2009-01-07, 19:28

Congrats! Out of curiosity, about how long would it take to definitively prove this prime?

philmoore · 2009-01-07, 19:52

Quote:

Originally Posted by Mini-Geek

Out of curiosity, about how long would it take to definitively prove this prime?

About 500 million years. I get around the same answer, either scaling up ECPP, or assuming the Generalized Riemann Hypothesis, and doing Miller-Rabin to all bases < 2(ln N)^2.

TimSorbet · 2009-01-07, 20:40

Quote:

Originally Posted by philmoore

About 500 million years. I get around the same answer, either scaling up ECPP, or assuming the Generalized Riemann Hypothesis, and doing Miller-Rabin to all bases < 2(ln N)^2.

Wow. I knew it'd be way too long to be practical, but that's REALLY long. Thanks.

CRGreathouse · 2009-01-07, 21:00

Quote:

Originally Posted by philmoore

About 500 million years. I get around the same answer, either scaling up ECPP, or assuming the Generalized Riemann Hypothesis, and doing Miller-Rabin to all bases < 2(ln N)^2.

But think -- if Moore's law continues until the GRH is proved a hundred years from now, it'll take under a millisecond to prove with Miller's test.

paleseptember · 2009-01-07, 21:34

<does the (probably) Prime Happy Dance!>

I am quite excited by this. Though I can't believe I missed the result. Argghhh! Have very carefully checked all my other results files now.

Time for one more Happy Dance? Yeah, I think so!

henryzz · 2009-01-07, 21:47

Quote:

Originally Posted by paleseptember

<does the (probably) Prime Happy Dance!>

I am quite excited by this. Though I can't believe I missed the result. Argghhh! Have very carefully checked all my other results files now.

Time for one more Happy Dance? Yeah, I think so!

nice dancing

paleseptember · 2009-01-07, 22:25

Quote:

Originally Posted by henryzz

nice dancing

Thanks! Not nearly so awesome as your avatar. That's some wicked turtle dancing ^_^

em99010pepe · 2009-01-07, 22:39

Congrats Ben!!!

(Copied the first post to Free-DC forum..lol)

Kman1293 · 2009-01-08, 00:32

Congratulations!

2009-01-07, 19:16	#1
philmoore "Phil" Sep 2002 Tracktown, U.S.A. 19·59 Posts	Record probable prime found! Congratulations to Ben Maloney (paleseptember) who discovered the probable prime $2^{1518191}+75353$ . At 457,022 decimal digits, it should soon appear as the new probable prime record at the website of Henri and Renaud Lifchitz, PRP Records, Probable Primes Top 10000. We have performed strong probable prime tests on this number to all 20 prime bases from 2 to 71. The probability that a random number of this size that passes even one strong probable prime test is composite is less than $10^{-728}$ . This eliminates the first of the five sequences, and should speed up our PRP testing by over 20% as well as our sieving by around 10%. I have already uploaded new work files and will get a new sieve file up soon as well. Thanks to everyone who contributed to this effort! And now for the embarrassing part - this prp actually showed up in early November, but was not noticed by either of us! In fact, PRP testing is currently approaching 630,000 digits, a good bit beyond this record. I visually scanned all of the results files when they came in, but obviously, out of the more than 300 results in this file, I overlooked the important one! Moral: computers make fewer mistakes than humans, so always search the file for the string "probable". Ben says he did search, but specified the wrong string. Unfortunately, it means that 20% of our PRP testing the past two months was unnecessary, but in the long run, that is probably a drop in the bucket compared to what comes next. All I can say is that it will not happen again! We are close to finishing PRP testing up to n=2^21, about 2.1 million. In the range from 2^21 to 2^22, I calculate that we should expect about 0.667 new primes. Let's go find another one!

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2009-01-07, 19:23	#2
engracio May 2007 11² Posts	Congratulation Ben and Phil. Great job. Let's find another one.

2009-01-07, 19:28	#3
TimSorbet Account Deleted "Tim Sorbera" Aug 2006 San Antonio, TX USA 11×389 Posts	Congrats! Out of curiosity, about how long would it take to definitively prove this prime?

2009-01-07, 21:34	#7
paleseptember Jun 2008 Wollongong, .au 3×61 Posts	<does the (probably) Prime Happy Dance!> I am quite excited by this. Though I can't believe I missed the result. Argghhh! Have very carefully checked all my other results files now. Time for one more Happy Dance? Yeah, I think so!

2009-01-07, 22:39	#10
em99010pepe Sep 2004 2·5·283 Posts	Congrats Ben!!! (Copied the first post to Free-DC forum..lol)

2009-01-08, 00:32	#11
Kman1293 Feb 2008 11 Posts	Congratulations!