PiHex

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PiHex was a distributed computing project organized by Colin Percival to calculate specific bits of Pi, the greatest calculation of Pi ever successfully attempted. 1,246 contributors used idle time slices on almost two thousand computers to make its calculations. They made use of Bellard's formula, a faster version of the BBP formula, with the algorithm discovered by Bailey, Borwein, and Plouffe in 1995.

After setting three records, calculating bits five trillion minus 3 through five trillion plus 76, forty trillion minus 3 through forty trillion plus 64, and one quadrillion minus 3 through one quadrillion plus 60 bits, the project ended on September 11, 2000.

Unlike most computations of Pi, which compute results in Base 10, PiHex computed Base 2 digits (bits); the BBP algorithm can only be used to compute Pi in Base 2.

Here are the final digit strings for each of the three calculations:

  • Binary digits of Pi from five trillion minus three to five trillion seventy-six (completed August 30, 1998):
00000111111001000101011100110011110011000111100100001011010110110101100101111001
  • Binary digits of Pi from forty trillion minus three to forty trillion sixty-four (February 9, 1999):
10100000111110011111111100110111000111010001011101011001001111100000
  • Binary digits of Pi from one quadrillion minus three to one quadrillion sixty (September 11, 2000):
1110011000100001011010110000011010011100101101101100000111010011

Therefore, the least significant known bit of Pi is 1 at position 1,000,000,000,000,060 (one quadrillion sixty) or 1015+60.

To calculate the five trillionth digit (and the following seventy-six digits) took 13,500 CPU hours, using 25 computers from 6 different countries. The forty trillionth digit required 84,500 CPU hours and 126 computers from 18 different countries. The highest calculation, the one quadrillionth digit, took 1.2 million CPU hours and 1,734 computers from 56 different countries. Total resources: 1,885 computers donated 1.3 million CPU hours. The average computer that was used to calculate would have taken 148 years to complete the calculations alone.

While the PiHex project calculated the least significant digits of Pi ever attempted in any base, second place is held by Shigeru Kondo who derived the 5 trillionth digit in base 10.