The 1000 billionth binary digit of PI is '1' !

After about one month of computation on more than twenty high-endworkstations and PCs, we can announce that:

The 1000 billionth (10^12) binary digits of PI are

1000 0111 1111 0111 0010 1011 0001 1101 1100 1001 0111 1000 0110 1001 0001 01001011 0001 0101 1011 0001 0110 1111 11101001 0010 0001 1000 1011 0000 0100 00101010 0011 1101 0100 0001 0000

[In the more compact hexadecimal notation, we obtain
87F72B1DC9786914B15B16FE9218B042A3D410].

The computation was carried out by using the algorithm described in On The RapidComputation of Various Polylogarithmic Constants by David Bailey,Peter Borwein, and Simon Plouffe. However, the slightly faster Bellard's binaryformula was used.

A generic parallel computation program was developped to handle thecommunications between the server and the clients. It has beendesigned to handle huge computations with small communications betweenthe server and the clients with a high reliability.

The first computation took 220 days of CPU time, and 12 days of realtime. A second computation was done to verify the first. We computedthe digits starting at offset (10^12)-9 using the same formula. Sincethe intermediate results are not correlated, this is a goodverification method. The second computation took 180 days of CPU timebecause of a better optimized code. The computer used were mainlyUltraSparc workstations. We used some Pentium PCs, DEC Alpha 200 and3000, and SGI10000 computers too.

I want to thank some friends who accepted to launch the program onsome idle computers they managed to find. In particular, I thankSamuel Orzan, Theresa Lam, Bruno Beaufils, Stephane Munier and LionelUlmer.

Sept 22 1997, Fabrice Bellard (bellard@email.enst.fr).