Prime counting function records - Page 4

dbaugh · 2015-03-11, 14:13

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.

dbaugh · 2015-11-25, 10:00

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

kwalisch · 2015-11-25, 12:46

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.

D. B. Staple · 2015-11-25, 13:40

Nice work, David! I'm glad to hear it.

danaj · 2015-11-25, 16:39

Thanks David, and well done to Kim and Douglas.

Jan Büthe has been publishing some nice work on tighter bounds lately.

Cybertronic · 2015-11-29, 05:30

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

dbaugh · 2015-11-30, 07:38

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.

CRGreathouse · 2015-12-02, 16:26

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.

danaj · 2015-12-02, 20:44

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.

CRGreathouse · 2015-12-07, 03:52

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!

XYYXF · 2016-12-25, 22:15

Quote:

Originally Posted by dbaugh

We should see pi(1e27) soon.

2015-11-29, 05:30	#39
Cybertronic Jan 2007 DEUTSCHLAND ! 437₈ 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

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2015-03-11, 14:13	#34
dbaugh Aug 2005 2×59 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 2·59 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 2²×5 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 38₁₆ Posts	Nice work, David! I'm glad to hear it.

2015-11-25, 16:39	#38
danaj "Dana Jacobsen" Feb 2011 Bangkok, TH 2²·227 Posts	Thanks David, and well done to Kim and Douglas. Jan Büthe has been publishing some nice work on tighter bounds lately.

2015-11-30, 07:38	#40
dbaugh Aug 2005 2·59 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, 20:44	#42
danaj "Dana Jacobsen" Feb 2011 Bangkok, TH 2²·227 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.