The Eight Quadrillionth Bit of π is 0

To celebrate Pi Day, one researcher has found more digits of the magical ratio than ever before. Using a serious number of NVIDIA graphics cards (30 to be precise), Ed Karrels pushed the current known digit count to 2,000,000,000,000,008.

To celebrate the 2013 π day, I’d like to announce a new record: the eight quadrillionth bit of π is 0!

OK, the odds of guessing that are pretty good, so how about more details?

Starting at the two quadrillionth hexadecimal digit (where each hexadecimal digit is four bits) the next eight digits of π are 653728f1.

All the computations were done on graphics cards rather than on regular CPUs. I spread the job across three sets of graphics card-enabled computers:

  • One computer with four NVIDIA GTX 690 graphics cards.
  • One computer with two NVIDIA GTX 680 graphics cards.
  • 24 computers (at Santa Clara University Design Center) with one NVIDIA GTX 570 graphics card each.

The initial run, targeting the 2,000,000,000,000,000th digit, took 35 days from December 19th to January 22nd. The doublecheck run, targeting the 2,000,000,000,000,008th digit, took 26 days from January 22nd to February 16th. The doublecheck run went faster because I used a newer version of the programming tools to build the program (CUDA compiler 5.0 versus 4.0).

The doublecheck run showed that 25 digits of the initial run were accurate. So I’ve got 25 new digits, but I’m only making the first eight public for now. That way, if and when someone else extends this result, I can help verify that they really did get accurate results in their computation. [karrelsblog]

I’d love to know how quickly Titan or another true supercomputer could find Pi to this many digits. The computing power used by Karrels isn’t anything special – given the same time frame, how many digits could Blue Gene/Q calculate?