20090901, 18:25  #1  
"Phil"
Sep 2002
Tracktown, U.S.A.
19·59 Posts 
Megadigit probable prime found, our third!
We have this news from Ben Maloney (paleseptember):
Quote:
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 10^{7} 50%  5.2 x 10^{8} 90%  5.5 x 10^{11} 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 20090902 at 14:13 Reason: new sieve file uploaded 

20090901, 18:55  #2 
Jan 2007
Germany
1010101000_{2} Posts 
Congratulation also !
I think we can proof all PRP within 1000 years, because one day we can proof with a better method. 
20090901, 19:39  #3 
Jun 2003
Ottawa, Canada
495_{16} 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. 
20090901, 21:55  #4 
Jun 2008
Wollongong, .au
B7_{16} Posts 
Thanks all, I'm incredibly happy about the find! (And no, Phil hasn't been feeding me the "good" workfiles :P)

20090901, 22:07  #5 
May 2007
11^{2} Posts 
Okay Ben you know the drill. Been thru this 3x.
Can't wait to be doing this again 
20090901, 23:45  #6 
Jun 2008
Wollongong, .au
3·61 Posts 
Engracio, I'm sorry! >.<

20090902, 00:11  #7 
May 2007
11^{2} Posts 

20090902, 00:39  #8 
"Phil"
Sep 2002
Tracktown, U.S.A.
461_{16} Posts 
???
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! Last fiddled with by philmoore on 20090902 at 16:06 Reason: added more waves, of course! 
20090902, 00:53  #9  
May 2007
171_{8} Posts 
Quote:
Ben you do have to buy the ticket to win. 

20090902, 01:29  #10 
Jun 2008
Wollongong, .au
3·61 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 highestweight 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!) 
20090902, 02:17  #11 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{2}·3^{2}·283 Posts 

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