From: kanada@pi.cc.u-tokyo.ac.jp (Yasumasa KANADA)
Subject: New world record of pi : 51.5 billion decimal digits

Dear pi people;

Now is the time for the announcement of new world record of pi. It tooklonger time than our expectation.Nearly two years has passed since we got new world record of 6.4 billion.Now, we got eight times more record than 6.4 billion as the following textswhich you can get with anonymous ftp to 'www.cc.u-tokyo.ac.jp'

Yasumasa KANADA, Computer Centre, University of Tokyo

Our latest record was established as follows:

Declared record: 51,539,600,000 decimal digits

Yasumasa KANADAand Daisuke TAKAHASHI

Two independent calculations based on two different algorithms generated51,539,607,552 (=3*2^34) decimal digits of pi and comparison of two generatedsequences matched 51,539,607,510 decimal digits, e.g., a 42 decimal digitsdifference. Then we are declaring 51,539,600,000 decimal digits as thenew world record.(See related lecture on Pi and Mathland article.)

Main program run:
Job start : 6th June 1997 22:29:06
Job end : 8th June 1997 03:32:17
Elapsed time : 29:03:11
 Main memory : 212 GB
Algorithm : Borweins' 4-th order convergent algorithm
(Run the algorithm.)
Verification program run:
Job start : 4th July 1997 22:11:42
Job end : 6th July 1997 11:19:58
Elapsed time : 37:08:16
 Main memory : 188 GB
Algorithm : Gauss-Legendre algorithm(Brent-Salamin)
Optimized main program run:
Job start : 1st August 1997 23:04:15
Job end : 3rd August 1997 00:18:47
Elapsed time : 25:14:32
Main memory : 212 GB
Algorithm : Borweins' 4-th order convergent algorithm
Machine used: HITACHI SR2201 at the Computer Centre, University of Tokyo,with 1024 Processors.
50,000,000,000-th digits of pi and 1/pi:

pi : 85133 98712 75109 30042
1/pi: 1191 08624 25640 78042

(First digit '3' for pi or '0' for 1/pi is not included in the above count.)

Frequency distribution for pi-3 up to 50,000,000,000 decimal places:

'0' : 5000012647; '1' : 4999986263; '2' : 5000020237; '3' : 4999914405
'4' : 5000023598; '5' : 4999991499; '6' : 4999928368; '7' : 5000014860
'8' : 5000117637; '9' : 4999990486;

Chi square = 5.60

Frequency distribution for 1/pi up to 50,000,000,000 decimal places:

'0' : 4999969955; '1' : 5000113699; '2' : 4999987893; '3' : 5000040906
'4' : 4999985863; '5' : 4999977583; '6' : 4999990916; '7' : 4999985552
'8' : 4999881183; '9' : 5000066450;

Chi square = 7.04
51,539,600,000-th digits of pi and 1/pi

pi : 70532 46569 86142 12904
1/pi: 0081 50624 62192 72973

(First digit '3' for pi or '0' for 1/pi is not included in the above count.)

Some interesting digit sequences

0123456789 : from 17,387,594,880-th of pi
0123456789 : from 26,852,899,245-th of pi
0123456789 : from 30,243,957,439-th of pi
0123456789 : from 34,549,153,953-th of pi
0123456789 : from 41,952,536,161-th of pi
0123456789 : from 43,289,964,000-th of pi

9876543210 : from 21,981,157,633-th of pi
9876543210 : from 29,832,636,867-th of pi
9876543210 : from 39,232,573,648-th of pi
9876543210 : from 42,140,457,481-th of pi
9876543210 : from 43,065,796,214-th of pi

09876543210 : from 42,321,758,803-th of pi
27182818284 : from 45,111,908,393-th of pi

0123456789 : from 6,214,876,462-th of 1/pi
01234567890 : from 50,494,465,695-th of 1/pi

9876543210 : from 15,603,388,145-th of 1/pi
9876543210 : from 51,507,034,812-th of 1/pi

999999999999 : from 12,479,021,132-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 Mr. Daisuke TAKAHASHI, a Research Associate atour Computer Centre.
Message passing routines were written by myself.
CPU used was the HITACHI SR2201 at the Computer Centre, University of Tokyo.
1024 PE's were definitely used through single job parallel processing fortotal of two programs run.

Yasumasa KANADA
Computer Centre, University of Tokyo
Bunkyo-ku Yayoi 2-11-16
Tokyo 113 Japan
Fax : +81-3-3814-7231 (office)
E-mail: kanada@pi.cc.u-tokyo.ac.jp
July 26:

QUESTION(JMB): Do you have an estimate for the same method

(i) in serial

ANSWER(YK): $\inf$ because we can't access machines with 256GBmain memory and minimum of 72 GB disk storage. (If we can access themachine with more memory, elapsed time is even shorter. Bothcalculations will be less than half a day with 300GFlops peakperformance machine.)

(ii) without fast multiplication?

ANSWER: $\inf$ because man-made machines can easily becollapsedor give incorrect answers with the duration of long longcalculations.