17th August 2009

Our latest record was established as the followings;

Declared record:
 2,576,980,370,000 decimal digits

 Two independent calculation based on two different algorithms
generated 2,576,980,377,600 (=75*2^35) decimal digits of pi and
comparison of two generated sequences matched up to 2,576,980,377,524
decimal digits, e.g., 76 decimal digits difference. Then we are
declaring 2,576,980,370,000 decimal digits as the new world record.

Main program run:
 Job start    :  9th April 2009 07:37:32 (JST)
 Job end      : 10th April 2009 12:43:21 (JST)
 Elapsed time : 29:05:49
 Main memory  : 13.5 TB
 Algorithm    : Gauss-Legendre algorithm

Verification program run:
 Job start    : 27th April 2009 21:35:36 (JST)
 Job end      : 29th April 2009 18:06:09 (JST)
 Elapsed time : 44:30:33
 Main memory  : 12.9 TB
 Algorithm    : Borwein's 4-th order convergent algorithm

2,500,000,000,000-th digits of pi and 1/pi:
 pi  : 7023378492 4587524911 1838622539 0987058051 8718886518
 1/pi: 0010432844 0001483439 6158108827 4408637842 1609987750
                                                            ^
                                           2,500,000,000,000-th
 (First digit '3' for pi or '0' for 1/pi is not included in the above count.)

Frequency distribution for pi-3 up to 2,500,000,000,000 decimal places:
 '0' : 249999192826; '1' : 249999959334; '2' : 250000751269;
 '3' : 249999904969; '4' : 250000455856; '5' : 249999721513;
 '6' : 249999564178; '7' : 249999660121; '8' : 250001040584;
 '9' : 249999749350; Chi-square = 11.85

Frequency distribution for 1/pi up to 2,500,000,000,000 decimal places:
 '0' : 249999622924; '1' : 250000603011; '2' : 249999024748;
 '3' : 249999886945; '4' : 250000566113; '5' : 250000389148;
 '6' : 250000066227; '7' : 249999751301; '8' : 250000370807;
 '9' : 249999718776; Chi-square = 8.90

2,576,980,370,000-th digits of pi and 1/pi:
 pi  : 3616276346 5152343138 0598550567 3249553206 9855284552
 1/pi: 1787760186 8492477551 0458174294 3077949861 4582392945
                                                            ^
                                           2,576,980,370,000-th
 (First digit '3' for pi or '0' for 1/pi is not included in the above count.)

Some of interesting digits sequences;

  012345678901 : from 1,781,514,067,534-th of pi
  012345678901 : from 2,364,190,386,673-th of pi

  987654321098 : from   593,100,546,152-th of pi
  987654321098 : from 1,116,106,038,318-th of pi

 8888888888888 : from 2,164,164,669,332-th of pi

  271828182845 : from 1,016,065,419,627-th of pi
  271828182845 : from 1,535,917,328,677-th of pi

  314159265358 : from 1,142,905,318,634-th of pi

  012345678901 : from   800,507,066,497-th of 1/pi
  012345678901 : from 1,266,229,196,919-th of 1/pi
  012345678901 : from 1,473,016,373,015-th of 1/pi
  012345678901 : from 1,816,975,999,322-th of 1/pi

  987654321098 : from   459,580,193,751-th of 1/pi
  987654321098 : from   865,156,153,180-th of 1/pi
  987654321098 : from 2,392,385,170,607-th of 1/pi

 3333333333333 : from    55,172,085,586-th of 1/pi
 4444444444444 : from   917,885,346,865-th of 1/pi
 4444444444444 : from 1,828,219,364,949-th of 1/pi

  271828182845 : from 1,400,850,126,381-th of 1/pi

 3141592653589 : from 1,801,642,919,402-th of 1/pi
 (First digit '3' for pi or '0' for 1/pi is not included in the above count.)

Programs were written by myself. The computer used was T2K Open
Supercomputer (Appro Xtreme-X3 Server) at the Center for Computational
Sciences, University of Tsukuba. 640 nodes of the total system (648
nodes, theoretical peak processing speed for the single node is 147.2
billion floating point operations per second. 95.4 trillion floating
point operations per second for all nodes), were definitely used as
single job and parallel processing for both of programs run.

Daisuke Takahashi
Graduate School of Systems and Information Engineering
University of Tsukuba
1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
E-mail: daisuke[at]cs.tsukuba.ac.jp