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 took longer 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 texts which 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:

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

Job start : 6th June 1997 22:29:06

Job end : 8th June 1997 03:32:17

Algorithm :

(Run the algorithm.)

Job start : 4th July 1997 22:11:42

Job end : 6th July 1997 11:19:58

Algorithm :

Job start : 1st August 1997 23:04:15

Job end : 3rd August 1997 00:18:47

Algorithm : Borweins' 4-th order convergent algorithm

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

'0' : 5000012647; '1' : 4999986263; '2' : 5000020237; '3' : 4999914405

'4' : 5000023598; '5' : 4999991499; '6' : 4999928368; '7' : 5000014860

'8' : 5000117637; '9' : 4999990486;

**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;

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

**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 at our Computer Centre.

Message passing routines were written by myself.

CPU used was the

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

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

**ANSWER**: $\inf$ because man-made machines can easily be
collapsed
or give incorrect answers with the duration of long long
calculations.