mersenneforum.org Megadigit probable prime found, our third!
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2009-09-01, 18:25   #1
philmoore

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

3×373 Posts
Megadigit probable prime found, our third!

We have this news from Ben Maloney (paleseptember):

Quote:
 This might cause some interest: [Tue Aug 25 08:20:40 2009] UID: paleseptember/borg, 2^4583176+2131 is a probable prime! Wd1: E1C99FEE,00000000
I have now done a few strong probable prime tests, and it has passed them all - three down, two to go!

At 1,379,674 decimal digits, this is the first known probable prime (on this planet) with over a million digits. I have submitted it to the Lifchitz website. It smashes our previous record found in January, with over twice as many digits.

Now for the statistics: This eliminates 30.2% of our prp tests, which should provide a significant increase in our speed. The remaining tests are divided about equally between 40291 (49.8% of the total) and 41693 (50.2% of the total). New work files have already been uploaded. I have also uploaded a new sieve file.

The probability that a random number of this size is composite after passing all these strong probable prime tests is < 10-1285.

To prove that this number is actually prime would take around 125 billion years if we could gear up ECPP on a single processor. On the other hand, if the Generalized Riemann Hypothesis could be proven, we could prove it is prime in only 40 billion years or so. Or with a billion processors, we could prove it is prime in around 40 years.

What are the chances now of solving this problem by finding the other two probable primes? We have been fortunate in eliminating the three lowest weight sequences first. I estimate our probabilities of solution given search limits on the exponents to be as follows:

10% - 2.07 x 107
50% - 5.2 x 108
90% - 5.5 x 1011

For each doubling of the exponent size, we can expect to find about .385 probable primes in that range. Our current sieve range goes up to 50 million, and we can expect to find about 1.32 more probable primes in this range. I estimate that in this range, we have about a 20.5% chance of finding both probable primes and finishing the problem, a 36.5% chance of finding exactly one more probable prime, and a 43% chance of finding nothing (but that's not going to happen!)

Here is a graph of the progress so far, and a comparison with the Sierpinski problem:

Congratulations, everyone!

Last fiddled with by philmoore on 2009-09-02 at 14:13 Reason: new sieve file uploaded

 2009-09-01, 18:55 #2 Cybertronic     Jan 2007 Germany 22·3·52 Posts Congratulation also ! I think we can proof all PRP within 1000 years, because one day we can proof with a better method.
 2009-09-01, 19:39 #3 Jeff Gilchrist     Jun 2003 Ottawa, Canada 22×293 Posts Congrats paleseptember again on another PRP find. Are you paying off Phil for him to feed you the good work files? Can you let me know which range you are thinking of reserving next? Congrats everyone on helping to eliminate all the other candidates to find this first megadigit PRP.
 2009-09-01, 21:55 #4 paleseptember     Jun 2008 Wollongong, .au 3×61 Posts Thanks all, I'm incredibly happy about the find! (And no, Phil hasn't been feeding me the "good" workfiles :P)
 2009-09-01, 22:07 #5 engracio     May 2007 112 Posts Okay Ben you know the drill. Been thru this 3x. Can't wait to be doing this again
 2009-09-01, 23:45 #6 paleseptember     Jun 2008 Wollongong, .au 18310 Posts Engracio, I'm sorry! >.<
2009-09-02, 00:11   #7
engracio

May 2007

1718 Posts

Quote:
 Originally Posted by paleseptember Engracio, I'm sorry! >.<
What no ???

Come on guys let's

Wohoooooo

2009-09-02, 00:39   #8
philmoore

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

3×373 Posts

Quote:
 Originally Posted by paleseptember >.<
???

?

And a hearty congratulations to Geoff and Kent for sieving, and for all our prp contributors since the last one: Engracio, Ben, Jeff, Serge, Geoff, Phil, and Dmitry!

Last fiddled with by philmoore on 2009-09-02 at 16:06 Reason: added more waves, of course!

2009-09-02, 00:53   #9
engracio

May 2007

112 Posts

Quote:
 Originally Posted by philmoore ??? How about And a hearty congratulations to Geoff and Kent for sieving, and for all our prp contributors since the last one: Engracio, Ben, Jeff, Serge, Geoff, Phil, and Dmitry!
There you go Phil, I think Ben is getting worried why he has been lucky 3x. What he doesn't know is that he will win the next lottery soon.

Ben you do have to buy the ticket to win.

 2009-09-02, 01:29 #10 paleseptember     Jun 2008 Wollongong, .au 18310 Posts Okay, let there be The Happy Dance! Huge huge thanks to the Valiant Sievers and to the other Knights of PRP. It's just a random statistical clumping, honestly. I'm so happy that the project is making such good progress. We're down to two sequences, the two highest-weight sequences, which tilts the numbers infinitesimally in the favour of better return. I may actually go out today and buy a lottery ticket. Or something :D I'll let you know whether I win. Time for one more Happy Dance? Yeah, why not? *grabs the hands of the Valiant Sievers and Knights of PRP* (yeah, okay, I've got the image of us all dressed in medieval outfits now, lances at the ready in case of dragons!)
 2009-09-02, 02:17 #11 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2·3·5·313 Posts

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