5 Trillion Digits of Pi - New World Record

By Alexander J. Yee & Shigeru Kondo

August 2, 2010

This page is just the announcement page.

The full version (with technical details) is here. (English Only)

On August 2, 2010, We have successfully completed the computation of Pi to 5,000,000,000,000 decimal places on a single desktop computer in record time.

This is 2.3 trillion digits more than the previous world record by Fabrice Bellard (December 2009). Therefore, we are declaring 5 trillion digits as the new world record. It was done using a program created by Alexander Yee and a desktop computer built by Shigeru Kondo.

A small portion of the computed digits are shown in the table below:

1415926535 8979323846 2643383279 5028841971 6939937510 : 50
5820974944 5923078164 0628620899 8628034825 3421170679 : 100

2962457053 9070959679 6673211870 6342459769 2128529850 : 999,999,999,950
2976735807 0882130902 2460461146 5810642210 6680122702 : 1,000,000,000,000

9354516713 6069123212 1286195062 3408400370 1793492657 : 1,999,999,999,950
8386341797 9368318191 5708299469 1313121384 3887908330 : 2,000,000,000,000

3840840269 5893047555 2627475826 8598006396 3215856883 : 2,699,999,989,950
9256371619 3901058063 3448436720 6294374587 7597230153 : 2,699,999,990,000
8012497961 5892988915 6174704230 3863302264 3931687863 : 2,699,999,990,050
3126006397 8582637253 6739664083 9716870851 0983536511 : 2,699,999,990,100

5628334110 5221005309 8638608325 4364661745 5833914321 : 2,999,999,999,950
9150024270 6285788691 0228572752 8179710957 7137931530 : 3,000,000,000,000

5209957313 0955102183 1080456596 1489168093 0578494464 : 3,999,999,999,950
3638467628 3610607856 5071920145 5255995193 8577295739 : 4,000,000,000,000

2597691971 6538537682 7963082950 0909387733 3987211875 : 4,999,999,999,950
6399906735 0873400641 7497120374 4023826421 9484283852 : 5,000,000,000,000

Validation File: Validation - Pi - 5,000,000,000,000.txt

Note that multicore efficiency % is inaccurate. The actual efficiency is about ~85%.

Computation Statistics - All times are Japan Standard Time (JST).

Pi - Computation
90 days

Start : 6:19 PM (JST) May 4, 2010
Finish: 1:12 AM (JST) August 3, 2010

Pi - Verification
64 hours (primary)
66 hours (secondary)

The main computation took 90 days on Shigeru Kondo's desktop. Verification was done using two separate computers.

Due to the size of this computation, a tremendous amount of memory was needed:

- Roughly 22 TB* of disk was needed to perform the computation.

- Another 3.8 TB of disk was needed to store the compressed output of decimal and hexadecimal digits.

If the digits were stored in an uncompressed ascii text file, the combined size of the decimal and hexadecimal digits would be 8.32 TB.

*TB = 2⁴⁰ bytes

The Software:

Software for Computation:

The program that was used for the main computation is y-cruncher v0.5.4.9138 Alpha.

See main page: y-cruncher - A Multi-Threaded Pi Program

y-cruncher is a powerful multi-threaded program/benchmark that is becoming an increasingly popular tool within the computer enthusiast community. It was also used for the current world record for most digits computed for several other famous constants. (These include: e, Square Root of 2, Golden Ratio, Euler-Mascheroni Constant, Natural Log of 2, Apery's Constant, and Catalan's Constant.)

There are several aspects of y-cruncher that set it apart from most other similar Pi-crunching programs:

It uses state-of-the-art algorithms to achieve never-before-seen computational speeds. Many of these methods and algorithms are newly developed and first-time tested in y-cruncher.
y-cruncher is highly scalable. Most other multi-threaded Pi programs are unable to scale past 4 cores. Therefore, they are unable to fully utilize many core machines such as the 12-core/24-thread computer that was used for this Pi computation.
y-cruncher supports the use of multiple hard drives to use as distributed memory storage for very large computations.
y-cruncher is fault-tolerant to hardware errors. It is able to detect and recover from most computational errors that are caused by hardware anomalies or instablity. This has proven invaluable for extremely long computations where the chance of hardware failure is non-negligible.

Software for Verification:

The program that was used for the verification is y-cruncher BBP v1.0.119.

See main page: y-cruncher BBP

This program implements the digit-extraction algorithm for Pi using the BBP formulas. It's sole purpose was to verify the main computation.

The Hardware:

Shigeru Kondo's computer had the following specifications:

Processor

2 x Intel Xeon X5680 @ 3.33 GHz - (12 physical cores, 24 hyperthreaded)

Memory

96 GB DDR3 @ 1066 MHz - (12 x 8 GB - 6 channels) - Samsung (M393B1K70BH1)

Motherboard

Asus Z8PE-D12

Hard Drives

1 TB SATA II (Boot drive) - Hitachi (HDS721010CLA332)
3 x 2 TB SATA II (Store Pi Output) - Seagate (ST32000542AS)
16 x 2 TB SATA II (Computation) - Seagate (ST32000641AS)

Raid Controller

2 x LSI MegaRaid SAS 9260-8i

Operating System

Windows Server 2008 R2 Enterprise x64

Pictures

Click to enlarge.

Technical Details

The full article that contains many of the technical details are here.

Questions or Comments

Contact me via e-mail. Or you can also find me on XtremeSystems Forums under the username: poke349

You can contact Shigeru Kondo at ja0hxv@calico.jp.

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