# Pi Computation Record

Fabrice Bellard
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 time:

- 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
2009.
## 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.

## Hardware

PC used during the computation:
- 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)

Backups were done using 2 TB hard disks (Seagate Barracuda LP 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.

## Operating System

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.
## Pi Software

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.
- (1)
- 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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