The pi(x) project : results and current computations

Last update : April 07 2001

Each computation in the pi(x) project includes the verification. The verification consists in computing pi(x+delta) (with delta a small value compared to x, usually delta = 108) using different parameters y and z than the one used to compute pi(x), and by computing the difference with a classical sieve.

Computation of pi(x) for x = 1023

 pi(1023) = ???

 Estimated total time (on PII 350) : 360 days (verification included) Number of chunks (verification included) 1076 Number of completed chunks 1076 (100%) Started : Mar. 09 2001 Ended : Not finished yet (see the note below) Version of pix.exe 1.6 Total real time : 220 days

 Contributor Percentage of the computation Number of chunks Shigeru Kondo (Japan) 50% 538 Patrick Demichel (France) 14.7% 158 Stephane Fintz (France) 11.4% 123 Kevin O'Hare (USA, California) 9.4% 101 David Baugh (USA, Houston) 3.7% 40 Pascal Sebah (France, Paris) 3.3% 35 Xavier Gourdon (France, Paris) 1.7% 19 Frank Clowes (USA) 1.4% 15 Michael Roedel 1.3% 14 Lalera (Austria) 1.1% 12 Greg Hogan (USA) 0.9% 10 Stefan Sarin (Sweden) 0.8% 9 Greg Shilders (USA) 0.6% 6 Mats Wernersson (Sweden) 0.3% 3 Laurent Desnogues (France) 0.3% 3 Vaughan Davies (Australia, Sydney) 0.2% 2 Jorge Rey Díaz de Rada (Spain, Malaga) 0.1% 1

Note : the computation of p(1023) revealed a problem which has not been solved yet. The computations gave p(1023) = 1925320391606818006727 and p(1023+108) = 1925320391606819893167. The difference between those two value is 1886440 and should be equal to 1886441. In other words, a difference of 1 exists in the global check. Internal checks were used but did not permit to locate the problem. I am currently trying hard to solve this problem. The pi(x) project is stopped until the solution has been found.

Computation of pi(x) for x = 4 ×1022

 pi(4×1022) = 783,964,159,847,056,303,858

 Estimated total time (on PII 350) : 250 days (verification included) Number of chunks (verification included) 747 Number of completed chunks 747 (100%) Started : Feb. 17 2001 Ended : Mar. 08 2001 Version of pix.exe 1.5 Total real time : 132 days

 Contributor Percentage of the computation Number of chunks Shigeru Kondo (Japan) 52.5% 392 Stephane Fintz (France) 28.5% 213 Patrick Demichel (France) 15.8% 118 Stefan Sarin 11.1% 83 Kevin O'Hare (USA, California) 8.6% 64 David Baugh (USA, Houston) 4.6% 34 Xavier Gourdon (France) 3.9% 29 Lalera (Austria) 2.4% 18 Frank Clowes (USA) 2.4% 18 Mats Wernersson (Sweden) 2.0% 15 Greg Shilders 1.5% 11 Laurent Desnogues (France) 1.2 % 9 Didier Boivin 0.7% 5 Pascal Sebah (France) 0.5% 4 Greg Hogan (USA) 0.5% 4

Computation of pi(x) for x = 2 ×1022

 pi(2×1022) = 397,382,840,070,993,192,736

 Estimated total time (on PII 350) : 150 days (verification included) Number of chunks (verification included) 452 Number of completed chunks 452 (100%) Started : Dec. 23 2000 Ended : Feb. 15 2001 Version of pix.exe 1.4 Total real time : 85 days

Special contributor : Patrick Demichel (see the note below).

 Contributor Percentage of the computation Number of chunks Lalera (Austria) 35.5% 162 Shigeru Kondo (Japan) 28.3% 129 Stephane Fintz (France) 15.1% 69 Jerry M Regnault (USA) 6.6% 30 Frank Clowes (USA) 6.4 % 29 Xavier Gourdon (France) 5.5% 25 Matt Ramey 3.5% 16 Mats Wernersson (Sweden) 2.8% 13 Thomas 2.8% 13 Evan M Adams 2% 9 Michael Roedel 1.1% 5 Laurent Desnogues 0.7 % 3

Note : 100% of the chunks were computed at Jan. 28 2001, but the global check (described at the beginning of this page) did not confirm the value at that time. Some internal checks were performed to test each chunk. Wrong chunks have been found, and as before, they appeared to come from a hardware problem during the computation. Internal important checks are now programmed and will permit to find rapidly wrong chunks in the future.

I want to thank especially Patrick Demichel here, who helped me to find the wrong chunks by replaying all the chunks on his machines... Thus he computed 100% of the chunks by himself and also permitted me to find the final wrong chunk (which was C-29).

Computation of pi(x) for x = 1022

 pi(1022) = 201,467,286,689,315,906,290

 Estimated total time (on PII 350) : 99 days (verification included) Number of chunks (verification included) 295 Number of completed chunks 295 (100%) Started : Dec. 10 2000 Ended : Dec. 22 2000 Version of pix.exe 1.3 Total real time : 57 days

 Contributor Percentage of the computation Number of chunks Patrick Demichel (France) 54.2% 160 Stephane Fintz (France) 13.9% 37 Frank Clowes (USA) 8.8 % 26 Jerry M Regnault (USA) 5.1% 15 Xavier Gourdon (France) 5.1% 15 Pascal Sebah (France) 4.4% 13 Matt Ramey 4.1% 12 Andrew Walker (USA) 2% 6 Mats Wernersson (Sweden) 1.4% 4 Laurent Desnogues (France) 1 % 3 Shyam Sunder Gupta (India) 0.7% 2 Lalera (Austria) 0.3% 1 Paul Pollack 0.3 % 1

Note : Some contributions were received from Frank Voisin but they appeared to be all wrong : an ïll" chip is probably the cause of the problem.

Patrick Demichel computed all the chunks of the parts B, C and D. Only the chunks not computed by other people were taken into account for the statistics of Demichel.

Computation of pi(x) for x = 4×1021

 pi(4×1021) = 82,103,246,362,658,124,007

 Estimated total time (on PII 350) : 57 days (verification included) Number of chunks (verification included) 171 Number of completed chunks 171 (100%) Started : Dec. 03 2000 Ended : Dec. 12 2000 Version of pix.exe 1.2 Total real time : 37 days

 Contributor Percentage of the computation Number of chunks Patrick Demichel (France) 61.4% 105 Xavier Gourdon (France) 12.8% 22 Pascal Sebah (France) 9.9% 17 Stephane Fintz (France) 6.4% 11 Laurent Desnogues (France) 4.6 % 8 Thomas Nokleby (Norway) 4.6 % 8

Note : As for the pi(2×1021), some problems occured in the computation. Some values computed by Patrick Demichel were wrong because of an ïll" chip... The same chunk ran several times of the same ïll" chip never gave the same values ! To prevent this kind of problems, more verification will be performed for future chunks.

Computation of pi(x) for x = 2×1021

 pi(2×1021) = 41,644,391,885,053,857,293

 Estimated total time (on PII 350) : 30 days +30 days for the verification. Number of chunks (verification included) 123 Number of completed chunks 123 (100%) Started : Nov. 6 2000 Ended : Dec. 01 2000 Version of pix.exe 1.1 Total real time : 35 days (verification included) Total equivalent time (on PII 350) : 55 days (verification included)

 Contributor Percentage of the computation Number of chunks Xavier Gourdon (France) 28.5% 35 Pascal Sebah (France) 27.6% 34 Alexandre Heimburger (France) 22.7% 28 Jani (Finland) 19.5% 24 Laurent Desnogues (France) 1.6 % 2

Note : The verification was done by Pascal Sebah and Xavier Gourdon only. It first releaved that a problem occured in the computation because the values did not agree. It appears in fact that the computation of the chunk A-10 was wrong. This bug is probably due to the local environnement of the contributor because another computation of the same chunk with the same program gave the right value.

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File translated from TEX by TTH, version 2.32.
On 15 Jan 2002, 23:56.