mersenneforum.org Prime counting function records
 Register FAQ Search Today's Posts Mark Forums Read

 2015-03-11, 14:13 #34 dbaugh     Aug 2005 112 Posts Douglas Staple programmed up a very good algorithm and he has some hella big computing power available. We should see pi(1e27) soon. I think pi(1e28) might best be a distributed project. That would be right up our alley.
 2015-11-25, 10:00 #35 dbaugh     Aug 2005 112 Posts Dear all, Using Kim Walisch's primecount program and 34 days on my BigRig computer, I have now independently confirmed Staple's result of pi(10^26) = 1699246750872437141327603. Best regards, David Baugh
 2015-11-25, 12:46 #36 kwalisch     Sep 2015 3×7 Posts Thanks David! Are few more details about the computation: pi(10^26) = 1,699,246,750,872,437,141,327,603 The computation took 34 days on David's dual socket server (36 CPU cores, Intel Xeon E5-2699 v3) which corresponds to 3.35 CPU cores years. The peak memory usage was about 117 gigabytes.
 2015-11-25, 13:40 #37 D. B. Staple     Nov 2007 Halifax, Nova Scotia 23·7 Posts Nice work, David! I'm glad to hear it.
 2015-11-25, 16:39 #38 danaj   "Dana Jacobsen" Feb 2011 Bangkok, TH 32×101 Posts Thanks David, and well done to Kim and Douglas. Jan Büthe has been publishing some nice work on tighter bounds lately.
 2015-11-29, 05:30 #39 Cybertronic     Jan 2007 Germany 49210 Posts Wow , this number pi(10^26) is correct. Many months ago, I found in a eMail-comment with another methode this number. 1,699,246,750,872,437,141,327,603 found by Guillimin and Briarée in 2014 .. was long ago. Norman http://www.mersenneforum.org/showthr...918#post388918 Last fiddled with by Cybertronic on 2015-11-29 at 05:36
 2015-11-30, 07:38 #40 dbaugh     Aug 2005 1718 Posts D. B. Staple first found the value using the supercomputers you mentioned. My post was to announce that it has now been independently confirmed. I think we both used the same essential method (combinatorial). I used Walisch's implementation and Staple used his own.
2015-12-02, 16:26   #41
CRGreathouse

Aug 2006

5,981 Posts

Quote:
 Originally Posted by danaj Jan Büthe has been publishing some nice work on tighter bounds lately.
I hadn't seen arXiv:1511.02032 before. Do you know why (1.9) in Theorem 2 is weaker than Korollar 5.3 in his thesis? The former has 27.57 in place of the latter's 2*9.7 = 19.4.

 2015-12-02, 20:44 #42 danaj   "Dana Jacobsen" Feb 2011 Bangkok, TH 32×101 Posts Kor 5.3 is defined for 10^8 < x < 10^19, while 1.9 is 2 <= x <= 10^19. Also 1.9's leading factor is $\frac{\sqrt{x}}{\log x}$ while Kor 5.3 would be $\sqrt{x} \over \log{\sqrt{x}}$ if I interpret the start of section 5.1 correctly.
2015-12-07, 03:52   #43
CRGreathouse

Aug 2006

5,981 Posts

Quote:
 Originally Posted by danaj Kor 5.3 is defined for 10^8 < x < 10^19, while 1.9 is 2 <= x <= 10^19. Also 1.9's leading factor is $\frac{\sqrt{x}}{\log x}$ while Kor 5.3 would be $\sqrt{x} \over \log{\sqrt{x}}$ if I interpret the start of section 5.1 correctly.
I accounted for the latter with my *2 above, but I didn't see the former. Thanks!

2016-12-25, 22:15   #44
XYYXF

Jan 2005
Minsk, Belarus

24·52 Posts

Quote:
 Originally Posted by dbaugh We should see pi(1e27) soon.

 Similar Threads Thread Thread Starter Forum Replies Last Post kwalisch Computer Science & Computational Number Theory 42 2022-08-12 10:48 Steve One Miscellaneous Math 8 2018-03-06 19:20 Steve One Miscellaneous Math 20 2018-03-03 22:44 SteveC Analysis & Analytic Number Theory 10 2016-10-14 21:48 pbewig Information & Answers 0 2011-07-14 00:47

All times are UTC. The time now is 16:55.

Fri Aug 19 16:55:04 UTC 2022 up 1 day, 14:23, 1 user, load averages: 1.39, 1.49, 1.49