Pi Computation Record
December 31st, 2009
I am pleased to announce a new world record for the computation of the
digits of Pi. The following number of digits were computed:
2242301460000 hexadecimal digits (base 16)
2699999990000 decimal digits (base 10)
The base 10 result needs about 1137 GB(1) of storage. Parts
of the result are available here.
Most of the computation was carried out on a single desktop computer
costing less than 2000 euros. The previous records since 1995 were done
using multi-million euro supercomputers.
- computation of the binary digits: 103 days
|Verification of the binary digits: 13 days
||Conversion to base 10: 12 days
||Verification of the conversion: 3 days
||Total: 131 days
The previous record of about 2577 billion
decimal digits was published by Daisuke Takahashi on August 17th
Formula and verification
The main computation used the Chudnovsky formula to give the binary
result. Then the binary result was converted to a base 10 result.
The binary result was verified with a formula found by the author with
the Bailey-Borwein-Plouffe algorithm which directly gives the n'th
hexadecimal digits of Pi. With this algorithm, the last 50 hexadecimal
digits of the binary result were checked. A checksum modulo a 64 bit
prime number done in the last multiplication of the Chudnovsky formula
evaluation ensured a negligible probability of error.
The conversion from binary to base 10 was verified with a checksum
modulo a 64 bit prime number.
More technical details are available here.
PC used during the computation:
Backups were done using 2 TB hard disks (Seagate Barracuda LP model).
- Core i7 CPU at 2.93 GHz
- 6 GiB (1) of RAM
- 7.5 TB of disk storage using five 1.5 TB hard disks (Seagate
Barracuda 7200.11 model)
The verification of the binary digits used a network of 9 Desktop PCs
during 34 hours. It could have been done on the same PC as the main
computation by using 13 more days.
The Linux Operating System was used with the 64 bit Red Hat Fedora 10
distribution. The 7.5 TB disk storage was managed using software
RAID-0 and the ext4 filesystem. Files of up to 2.5 TB were manipulated
during the computation.
All the software was written by the author. The most important part is
an arbitrary-precision arithmetic library able to manipulate huge
numbers stored on hard disks. Technical details are available here.
- The standard SI and binary prefixes are used. For example:
- 1 GB = 10^9 bytes
- 1 TB = 10^12 bytes
- 1 GiB = 2^30 bytes (approx. 1.07 GB)
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