The Bits of π
The table on the right are the results computed by distbbp.
- Row 0 to Row 7
- They were computed by a single machine.
- A single run of Row 7 took several seconds.
- Row 8 to Row 14
- They were computed by a 7600-task-capacity cluster.
- A single run of Row 14 took 27 hours.
- The computations in Row 13 and Row 14 were completed on May 20, 2009.
It seems that the corresponding bits were never computed before.
- The first part of Row 15 (6216B06)
- The first 30% of the computation was done in idle cycles of some
clusters spread over 20 days.
- The remaining 70% was finished over a weekend on Hammer,
a 30,000-task-capacity cluster, which was also used for the
petabyte sort benchmark.
- The log files are available
here.
- The result was posted in
this YDN blog.
- The second part of Row 15 (D3611)
- The starting position is 1,000,000,000,000,053, totally 20 bits.
- Two computations, at positions n and n+4, were performed.
- A single computation was divided into 14,000 jobs
and totally 7,000,000 tasks.
It took 208 years of CPU-time
or 12 days of cluster (with 7600-task-capacity) time.
- The log files are available
here.
- The computations were completed on June 30, 2009.
The last bit, the 1,000,000,000,000,072nd bit,
probably is the highest bit (or the least significant bit) of π
computed ever in the history.
| |
| Position n | π bits (in hex) starting at n |
0 | 1 | 243F6A8885A3* |
1 | 11 | FDAA22168C23 |
2 | 101 | 3707344A409 |
3 | 1,001 | 574E69A458F |
4 | 10,001 | 44EC5716F2B |
5 | 100,001 | 944F7A204 |
6 | 1,000,001 | 6FFFA4103 |
7 | 10,000,001 | 6CFDD54E3 |
8 | 100,000,001 | A306CFA7 |
9 | 1,000,000,001 | 3E08FF2B |
10 | 10,000,000,001 | 0A8BD8C0 |
11 | 100,000,000,001 | B2238C1 |
12 | 1,000,000,000,001 | 0FEE563 |
13 | 10,000,000,000,001 | 896DC3 |
14 | 100,000,000,000,001 | C216EC |
15 | 1,000,000,000,000,001 | 6216B06 ... D3611 |
*
By representing π in decimal, hexadecimal and binary, we have
π | = | 3.1415926535 8979323846 2643383279 ... |
| = | 3.243F6A8885 A308D31319 8A2E037073 ... |
| = | 11.0010010000 1111110110 1010100010 ... |
The first ten bits of π are 0010010000.
|