Chronology of computation of π explained

The table below is a brief chronology of computed numerical values of, or bounds on, the mathematical constant pi . For more detailed explanations for some of these calculations, see Approximations of .

As of July 2024, has been calculated to 202 trillion decimal digits. The last 100 decimal digits of the latest world record computation are:[1] 7034341087 5351110672 0525610978 1945263024 9604509887 5683914937 4658179610 2004394122 9823988073 3622511852

Before 1400

DateWhoDescription/Computation method usedValueDecimal places
(world records
in bold)
2000? BCAncient Egyptians[2] 4 × 23.1605...1
2000? BCAncient Babylonians3 + 3.1251
2000? BCAncient Sumerians[3] 3 + 23/2163.10651
1200? BCAncient Chinese330
800–600 BC Shatapatha Brahmana – 7.1.1.18 [4] Instructions on how to construct a circular altar from oblong bricks:

"He puts on (the circular site) four (bricks) running eastwards 1; two behind running crosswise (from south to north), and two (such) in front. Now the four which he puts on running eastwards are the body; and as to there being four of these, it is because this body (of ours) consists, of four parts 2. The two at the back then are the thighs; and the two in front the arms; and where the body is that (includes) the head."[5]

= 3.1251
800? BCShulba Sutras[6] [7] [8] 23.088311 ...0
550? BCBible (1 Kings 7:23)"...a molten sea, ten cubits from the one brim to the other: it was round all about,... a line of thirty cubits did compass it round about"30
434 BCAnaxagoras attempted to square the circle[9] compass and straightedgeAnaxagoras did not offer a solution0
400 BC to AD 400 Vyasa[10] verses: 6.12.40-45 of the Bhishma Parva of the Mahabharata offer:
"...
The Moon is handed down by memory to be eleven thousand yojanas in diameter. Its peripheral circle happens to be thirty three thousand yojanas when calculated.
...
The Sun is eight thousand yojanas and another two thousand yojanas in diameter. From that its peripheral circle comes to be equal to thirty thousand yojanas.
..."
30
c. 250 BCArchimedes < < 3.140845... <  < 3.142857...2
15 BCVitruvius3.1251
Between 1 BC and AD 5Liu Xin[11] [12] Unknown method giving a figure for a jialiang which implies a value for ≈ .3.1547...1
AD 130Zhang Heng (Book of the Later Han) = 3.162277...
3.1622...1
150Ptolemy3.141666...3
250Wang Fan3.155555...1
263Liu Hui3.141024 < < 3.142074
3.14163
400He Chengtian3.142885...2
480Zu Chongzhi3.1415926 < < 3.1415927
3.14159267
499Aryabhata3.14163
640Brahmagupta3.162277...1
800Al Khwarizmi3.14163
1150Bhāskara II and 3.14163
1220Fibonacci3.1418183
1320Zhao Youqin3.1415926

1400–1949

DateWhoNoteDecimal places
All records from 1400 onwards are given as the number of correct decimal places.
1400Madhava of SangamagramaDiscovered the infinite power series expansion of,
now known as the Leibniz formula for pi[13]
10
1424Jamshīd al-Kāshī[14] 16
1573Valentinus Otho6
1579François Viète[15] 9
1593Adriaan van Roomen[16] 15
1596Ludolph van Ceulen20
161532
1621Willebrord Snell (Snellius)Pupil of Van Ceulen35
1630Christoph Grienberger[17] [18] 38 <-- calculated=39; determined=38 -->
1654Christiaan HuygensUsed a geometrical method equivalent to Richardson extrapolation10
1665Isaac Newton16
1681Takakazu Seki[19] 11
16
1699Abraham SharpCalculated pi to 72 digits, but not all were correct71
1706John Machin100
1706William JonesIntroduced the Greek letter ''
1719Thomas Fantet de LagnyCalculated 127 decimal places, but not all were correct112
1721AnonymousCalculation made in Philadelphia, Pennsylvania, giving the value of pi to 154 digits, 152 of which were correct. First discovered by F. X. von Zach in a library in Oxford, England in the 1780s, and reported to Jean-Étienne Montucla, who published an account of it.[20] 152
1722Toshikiyo Kamata24
1722Katahiro Takebe41
1739Yoshisuke Matsunaga51
1748Leonhard EulerUsed the Greek letter '' in his book Introductio in Analysin Infinitorum and assured its popularity.
1761Johann Heinrich LambertProved that is irrational
1775EulerPointed out the possibility that might be transcendental
1789Jurij Vega[21] Calculated 140 decimal places, but not all were correct126
1794Adrien-Marie LegendreShowed that 2 (and hence) is irrational, and mentioned the possibility that might be transcendental.
1824William RutherfordCalculated 208 decimal places, but not all were correct152
1844Zacharias Dase and StrassnitzkyCalculated 205 decimal places, but not all were correct200
1847Thomas ClausenCalculated 250 decimal places, but not all were correct248
1853Lehmann261
1853Rutherford440
1853William Shanks[22] Expanded his calculation to 707 decimal places in 1873, but an error introduced at the beginning of his new calculation rendered all of the subsequent digits invalid (the error was found by D. F. Ferguson in 1946).527
1882Ferdinand von LindemannProved that is transcendental (the Lindemann–Weierstrass theorem)
1897The U.S. state of IndianaCame close to legislating the value 3.2 (among others) for . House Bill No. 246 passed unanimously. The bill stalled in the state Senate due to a suggestion of possible commercial motives involving publication of a textbook.[23]
1910Srinivasa RamanujanFound several rapidly converging infinite series of, which can compute 8 decimal places of with each term in the series. Since the 1980s, his series have become the basis for the fastest algorithms currently used by Yasumasa Kanada and the Chudnovsky brothers to compute .
1946D. F. FergusonMade use of a desk calculator[24] 620
1947Ivan NivenGave a very elementary proof that is irrational
January 1947D. F. FergusonMade use of a desk calculator710
September 1947D. F. FergusonMade use of a desk calculator808
1949Levi B. Smith and John WrenchMade use of a desk calculator1,120

1949–2009

DateWhoImplementationTimeDecimal places
All records from 1949 onwards were calculated with electronic computers.
September 1949G. W. Reitwiesner et al. The first to use an electronic computer (the ENIAC) to calculate [25] 70 hours2,037
1953Kurt MahlerShowed that is not a Liouville number
1954S. C. Nicholson & J. JeenelUsing the NORC[26] 13 minutes3,093
1957George E. FeltonFerranti Pegasus computer (London), calculated 10,021 digits, but not all were correct[27] [28] 33 hours7,480
January 1958Francois GenuysIBM 704[29] 1.7 hours10,000
May 1958George E. FeltonPegasus computer (London)33 hours10,021
1959Francois GenuysIBM 704 (Paris)[30] 4.3 hours16,167
1961Daniel Shanks and John WrenchIBM 7090 (New York)[31] 8.7 hours100,265
1961J.M. GerardIBM 7090 (London)39 minutes20,000
February 1966Jean Guilloud and J. FilliatreIBM 7030 (Paris)41.92 hours250,000
1967Jean Guilloud and M. DichamptCDC 6600 (Paris)28 hours500,000
1973Jean Guilloud and Martine BouyerCDC 760023.3 hours1,001,250
1981Kazunori Miyoshi and Yasumasa KanadaFACOM M-200137.3 hours2,000,036
1981Jean GuilloudNot known2,000,050
1982Yoshiaki TamuraMELCOM 900II7.23 hours2,097,144
1982Yoshiaki Tamura and Yasumasa KanadaHITAC M-280H2.9 hours4,194,288
1982Yoshiaki Tamura and Yasumasa KanadaHITAC M-280H6.86 hours8,388,576
1983Yasumasa Kanada, Sayaka Yoshino and Yoshiaki TamuraHITAC M-280H<30 hours16,777,206
October 1983Yasunori Ushiro and Yasumasa KanadaHITAC S-810/2010,013,395
October 1985Bill GosperSymbolics 367017,526,200
January 1986David H. BaileyCRAY-228 hours29,360,111
September 1986Yasumasa Kanada, Yoshiaki TamuraHITAC S-810/206.6 hours33,554,414
October 1986Yasumasa Kanada, Yoshiaki TamuraHITAC S-810/2023 hours67,108,839
January 1987Yasumasa Kanada, Yoshiaki Tamura, Yoshinobu Kubo and othersNEC SX-235.25 hours134,214,700
January 1988Yasumasa Kanada and Yoshiaki TamuraHITAC S-820/80[32] 5.95 hours201,326,551
May 1989Gregory V. Chudnovsky & David V. ChudnovskyCRAY-2 & IBM 3090/VF480,000,000
June 1989Gregory V. Chudnovsky & David V. ChudnovskyIBM 3090535,339,270
July 1989Yasumasa Kanada and Yoshiaki TamuraHITAC S-820/80536,870,898
August 1989Gregory V. Chudnovsky & David V. ChudnovskyIBM 30901,011,196,691
19 November 1989Yasumasa Kanada and Yoshiaki TamuraHITAC S-820/80[33] 1,073,740,799
August 1991Gregory V. Chudnovsky & David V. ChudnovskyHomemade parallel computer (details unknown, not verified) [34] 2,260,000,000
18 May 1994Gregory V. Chudnovsky & David V. ChudnovskyNew homemade parallel computer (details unknown, not verified)4,044,000,000
26 June 1995Yasumasa Kanada and Daisuke TakahashiHITAC S-3800/480 (dual CPU) [35] 3,221,220,000
1995Simon PlouffeFinds a formula that allows the th hexadecimal digit of pi to be calculated without calculating the preceding digits.
28 August 1995Yasumasa Kanada and Daisuke TakahashiHITAC S-3800/480 (dual CPU) [36] [37] 56.74 hours?4,294,960,000
11 October 1995Yasumasa Kanada and Daisuke TakahashiHITAC S-3800/480 (dual CPU) [38] 116.63 hours6,442,450,000
6 July 1997Yasumasa Kanada and Daisuke TakahashiHITACHI SR2201 (1024 CPU) [39] [40] 29.05 hours51,539,600,000
5 April 1999Yasumasa Kanada and Daisuke TakahashiHITACHI SR8000 (64 of 128 nodes) [41] [42] 32.9 hours68,719,470,000
20 September 1999Yasumasa Kanada and Daisuke TakahashiHITACHI SR8000/MPP (128 nodes) [43] [44] 37.35 hours206,158,430,000
24 November 2002Yasumasa Kanada & 9 man teamHITACHI SR8000/MPP (64 nodes), Department of Information Science at the University of Tokyo in Tokyo, Japan[45] 600 hours1,241,100,000,000
29 April 2009Daisuke Takahashi et al.T2K Open Supercomputer (640 nodes), single node speed is 147.2 gigaflops, computer memory is 13.5 terabytes, Gauss–Legendre algorithm, Center for Computational Sciences at the University of Tsukuba in Tsukuba, Japan[46] 29.09 hours2,576,980,377,524

2009–present

DateWhoImplementationTimeDecimal places
All records from Dec 2009 onwards are calculated and verified on commodity x86 computers with commercially available parts. All use the Chudnovsky algorithm for the main computation, and Bellard's formula, the Bailey–Borwein–Plouffe formula, or both for verification.
31 December 2009Fabrice Bellard[47]
  • 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)
  • 64 bit Red Hat Fedora 10 distribution
  • Computation of the binary digits (Chudnovsky algorithm): 103 days
  • Verification of the binary digits (Bellard's formula): 13 days
  • Conversion to base 10: 12 days
  • Verification of the conversion: 3 days
  • Verification of the binary digits used a network of 9 Desktop PCs during 34 hours.
131 days2,699,999,990,000
= -
2 August 2010Shigeru Kondo[48]
  • using y-cruncher[49] 0.5.4 by Alexander Yee
  • with 2× Intel Xeon X5680 @ 3.33 GHz – (12 physical cores, 24 hyperthreaded)
  • 96 GiB DDR3 @ 1066 MHz – (12× 8 GiB – 6 channels) – Samsung (M393B1K70BH1)
  • 1 TB SATA II (Boot drive) – Hitachi (HDS721010CLA332), 3× 2 TB SATA II (Store Pi Output) – Seagate (ST32000542AS) 16× 2 TB SATA II (Computation) – Seagate (ST32000641AS)
  • Windows Server 2008 R2 Enterprise x64
  • Computation of binary digits: 80 days
  • Conversion to base 10: 8.2 days
  • Verification of the conversion: 45.6 hours
  • Verification of the binary digits: 64 hours (Bellard formula), 66 hours (BBP formula)
  • Verification of the binary digits were done simultaneously on two separate computers during the main computation. Both computed 32 hexadecimal digits ending with the 4,152,410,118,610th.[50]
90 days5,000,000,000,000
=
17 October 2011Shigeru Kondo[51]
  • using y-cruncher 0.5.5 by Alexander Yee
  • Verification: 1.86 days (Bellard formula) and 4.94 days (BBP formula)
371 days10,000,000,000,050
= + 50
28 December 2013Shigeru Kondo[52]
  • using y-cruncher 0.6.3 by Alexander Yee
  • with 2× Intel Xeon E5-2690 @ 2.9 GHz – (16 physical cores, 32 hyperthreaded)
  • 128 GiB DDR3 @ 1600 MHz – 8× 16 GiB – 8 channels
  • Windows Server 2012 x64
  • Verification using Bellard's formula: 46 hours
94 days12,100,000,000,050
= + 50
8 October 2014Sandon Nash Van Ness "houkouonchi"[53]
  • using y-cruncher 0.6.3 by Alexander Yee
  • with 2× Xeon E5-4650L @ 2.6 GHz
  • 192 GiB DDR3 @ 1333 MHz
  • 24× 4 TB + 30× 3 TB
  • Verification using Bellard's formula: 182 hours
208 days13,300,000,000,000
=
11 November 2016Peter Trueb[54] [55]
  • using y-cruncher 0.7.1 by Alexander Yee
  • with 4× Xeon E7-8890 v3 @ 2.50 GHz (72 cores, 144 threads)
  • 1.25 TiB DDR4
  • 20× 6 TB
  • Verification using Bellard's formula: 28 hours[56]
105 days22,459,157,718,361
14 March 2019Emma Haruka Iwao[57]
  • using y-cruncher v0.7.6
  • Computation: 1× n1-megamem-96 (96 vCPU, 1.4 TB) with 30 TB of SSD
  • Storage: 24× n1-standard-16 (16 vCPU, 60 GB) with 10 TB of SSD
  • Verification: 20 hours using Bellard's 7-term formula, and 28 hours using Plouffe's 4-term formula
121 days31,415,926,535,897
29 January 2020Timothy Mullican[58] [59]
  • using y-cruncher v0.7.7
  • Computation: 4× Intel Xeon CPU E7-4880 v2 @ 2.50 GHz
  • 320 GB DDR3 PC3-8500R ECC RAM
  • 48× 6 TB HDDs (Computation) + 47× LTO Ultrium 5 1.5 TB Tapes (Checkpoint Backups) + 12× 4 TB HDDs (Digit Storage)
  • Verification: 17 hours using Bellard's 7-term formula, 24 hours using Plouffe's 4-term formula
303 days50,000,000,000,000
=
14 August 2021Team DAViS of the University of Applied Sciences of the Grisons[60] [61]
  • using y-cruncher v0.7.8
  • Computation: AMD Epyc 7542 @ 2.9 GHz
  • 1 TiB of memory
  • 38× 16 TB HDDs (Of those, 34 are used for swapping and 4 used for storage)
  • Verification using the 4-term BBP formula: 34 hours
108 days62,831,853,071,796
21 March 2022Emma Haruka Iwao[62] [63]
  • using y-cruncher v0.7.8
  • Computation: n2-highmem-128 (128 vCPU and 864 GB RAM)
  • Storage: 663 TB
  • Verification: 12.6 hours using BBP formula
158 days100,000,000,000,000
=
18 April 2023Jordan Ranous[64] [65]
  • using y-cruncher v0.7.10
  • Computation: 2 x AMD EPYC 9654 (96 cores, 1.5 TiB RAM)
  • Storage: 583 TB (19× 30.72 TB)
59 days100,000,000,000,000
=
14 March 2024Jordan Ranous, Kevin O’Brien and Brian Beeler[66] [67]
  • using y-cruncher v0.8.3
  • Computation: 2 x AMD EPYC 9754 (128 cores, 1.5 TiB RAM)
  • Storage: 1,105 TB (36× 30.72 TB)
75 days105,000,000,000,000
=
28 June 2024Jordan Ranous, Kevin O’Brien and Brian Beeler[68] [69]
  • using y-cruncher v0.8.3
  • Computation: 2 x Intel Xeon Platinum 8592+ (128 cores, 1.0 TiB RAM)
  • Storage: 1.5 PB (28× 61.44 TB)
104 days202,112,290,000,000
=

See also

External links

Notes and References

  1. Web site: y-cruncher validation file .
  2. David H. Bailey . Jonathan M. Borwein . Peter B. Borwein . Simon Plouffe . 1997. The quest for pi. Mathematical Intelligencer. 19. 1. 50–57. 10.1007/BF03024340. 14318695.
  3. Web site: 2022-03-14 . Origins: 3.14159265... . 2022-06-08 . Biblical Archaeology Society . en.
  4. Book: Eggeling, Julius. The Satapatha-brahmana, according to the text of the Madhyandina school. 1882–1900. Oxford, The Clarendon Press. Princeton Theological Seminary Library. 1882. 302–303.
  5. Book: The Sacred Books of the East: The Satapatha-Brahmana, pt. 3. 1894. Clarendon Press. 303.
  6. Web site: 4 II. Sulba Sutras. www-history.mcs.st-and.ac.uk.
  7. Ravi P. Agarwal . Hans Agarwal . Syamal K. Sen . 2013 . Birth, growth and computation of pi to ten trillion digits . . 2013 . 100 . 10.1186/1687-1847-2013-100 . free .
  8. Book: Plofker, Kim. 18. Mathematics in India. Mathematics in India (book). 2009. Princeton University Press. 978-0691120676.
  9. Web site: Wilson . David . The History of Pi . sites.math.rutgers.edu . University Of Rutgers . https://web.archive.org/web/20230507165826/https://sites.math.rutgers.edu/~cherlin/History/Papers2000/wilson.html . 7 May 2023 . en . 2000 . live.
  10. Jadhav. Dipak. 2018-01-01. On The Value Implied In The Data Referred To In The Mahābhārata for π. Vidyottama Sanatana: International Journal of Hindu Science and Religious Studies. 2. 1. 18. 10.25078/ijhsrs.v2i1.511. 146074061. 2550-0651. free.
  11. Book: 趙良五. 中西數學史的比較. 1991. 臺灣商務印書館. 978-9570502688. Google Books.
  12. Needham, Joseph (1986). Science and Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth. Taipei: Caves Books, Ltd. Volume 3, 100.
  13. A. K.. Bag. 1980. Indian Literature on Mathematics During 1400–1800 A.D.. Indian Journal of History of Science. 15. 1. 86. ≈ 2,827,433,388,233/9×10−11 = 3.14159 26535 92222..., good to 10 decimal places..
  14. approximated 2π to 9 sexagesimal digits. Al-Kashi, author: Adolf P. Youschkevitch, chief editor: Boris A. Rosenfeld, p. 256 Azarian . Mohammad K. . Al-Risāla Al-Muhītīyya: A Summary . Missouri Journal of Mathematical Sciences . 2010 . 22 . 2 . 64–85 . 10.35834/mjms/1312233136. free.
  15. Book: Viète, François . François Viète . Canon mathematicus seu ad triangula : cum adpendicibus . 1579 . la .
  16. Book: {{lang|la|Romanus}}, {{lang|la|Adrianus}} . Ideae mathematicae pars prima, sive methodus polygonorum . 1593 . apud Ioannem Keerbergium . 2027/ucm.5320258006 . la .
  17. Book: Grienbergerus, Christophorus . Christoph Grienberger . la . 1630 . Elementa Trigonometrica . dead . https://web.archive.org/web/20140201234124/http://librarsi.comune.palermo.it/gesuiti2/06.04.01.pdf . 2014-02-01 .
  18. Book: Ernest William . Hobson . E. W. Hobson . 1913 . 'Squaring the Circle': a History of the Problem . 27 . Cambridge University Press . PDF.
  19. Book: Yoshio. Yoshio Mikami. Mikami. Eugene Smith. David . 1914. 2004. A History of Japanese Mathematics. paperback. Dover Publications. 0-486-43482-6.
  20. Benjamin Wardhaugh, "Filling a Gap in the History of : An Exciting Discovery", Mathematical Intelligencer 38(1) (2016), 6-7
  21. Vega . Géorge . 1795 . 1789 . Detérmination de la demi-circonférence d'un cercle dont le diameter est, exprimée en figures decimals . Nova Acta Academiae Scientiarum Petropolitanae . 11 . Supplement . 41–44 .

    Web site: Sandifer . Ed . 2006 . Why 140 Digits of Pi Matter . Southern Connecticut State University . dead . 2012-02-04 . https://web.archive.org/web/20120204040635/http://www.southernct.edu/~sandifer/Ed/History/Preprints/Talks/Jurij%20Vega/Vega%20math%20script.pdf .

  22. Hayes . Brian . Pencil, Paper, and Pi . 102 . 5 . 342 . . September 2014 . 13 February 2022 . 10.1511/2014.110.342.
  23. Web site: Indiana Bill sets value of Pi to 3. Lopez-Ortiz. Alex. February 20, 1998. the news.answers WWW archive. Department of Information and Computing Sciences, Utrecht University. 2009-02-01. 2005-01-09. https://web.archive.org/web/20050109144036/http://www.cs.uu.nl/wais/html/na-dir/sci-math-faq/indianabill.html. dead.
  24. Book: Wells, D. G. . The Penguin Dictionary of Curious and Interesting Numbers . May 1, 1998 . Penguin Books . 978-0140261493 . Revised . 33.
  25. G. . Reitwiesner . An ENIAC determination of π and e to more than 2000 decimal places . MTAC . 4 . 1950 . 11–15 . 10.1090/S0025-5718-1950-0037597-6 . free .
  26. S. C. . Nicholson . J. . Jeenel . Some comments on a NORC computation of π . MTAC . 9 . 1955 . 162–164 . 10.1090/S0025-5718-1955-0075672-5 . free .
  27. G. E. Felton, "Electronic computers and mathematicians," Abbreviated Proceedings of the Oxford Mathematical Conference for Schoolteachers and Industrialists at Trinity College, Oxford, April 8–18, 1957, pp. 12–17, footnote pp. 12–53. This published result is correct to only 7480D, as was established by Felton in a second calculation, using formula (5), completed in 1958 but apparently unpublished. For a detailed account of calculations of π see J. W. Jr. . Wrench . The evolution of extended decimal approximations to π . The Mathematics Teacher . 53 . 1960 . 644–650 . 8. 10.5951/MT.53.8.0644 . 27956272 .
  28. Book: Arndt . Jörg . Haenel . Christoph . Pi - Unleashed . 2001 . Springer . 978-3-642-56735-3 . en.
  29. F. . Genuys . Dix milles decimales de π . Chiffres . 1 . 1958 . 17–22 .
  30. This unpublished value of x to 16167D was computed on an IBM 704 system at the French Alternative Energies and Atomic Energy Commission in Paris, by means of the program of Genuys
  31. Daniel . Shanks . John W. J.r . Wrench . Calculation of π to 100,000 decimals . . 16 . 1962 . 77 . 76–99 . 10.1090/S0025-5718-1962-0136051-9 . free .
  32. Book: Kanada, Y. . Proceedings Supercomputing Vol.II: Science and Applications . Vectorization of multiple-precision arithmetic program and 201,326,000 decimal digits of pi calculation . November 1988 . https://ieeexplore.ieee.org/document/74139 . 117–128 vol.2 . 10.1109/SUPERC.1988.74139. 0-8186-8923-4 . 122820709 .
  33. Web site: Computers . 2022-08-04 . Science News . 24 August 1991 . en-US.
  34. Bigger slices of Pi (determination of the numerical value of pi reaches 2.16 billion decimal digits) Science News 24 August 1991 http://www.encyclopedia.com/doc/1G1-11235156.html
  35. ftp://pi.super-computing.org/README.our_last_record_3b
  36. ftp://pi.super-computing.org/README.our_last_record_4b
  37. Web site: GENERAL COMPUTATIONAL UPDATE . 2022-08-04 . www.cecm.sfu.ca.
  38. ftp://pi.super-computing.org/README.our_last_record_6b
  39. ftp://pi.super-computing.org/README.our_last_record_51b
  40. Web site: 2005-12-24 . Record for pi : 51.5 billion decimal digits . 2022-08-04 . https://web.archive.org/web/20051224015531/http://oldweb.cecm.sfu.ca/personal/jborwein/Kanada_50b.html . 2005-12-24 .
  41. ftp://pi.super-computing.org/README.our_last_record_68b
  42. Web site: Kanada . Yasumasa . plouffe.fr/simon/constants/Pi68billion.txt . www.plouffe.fr . https://web.archive.org/web/20220805103137/https://www.plouffe.fr/simon/constants/Pi68billion.txt . 5 August 2022 . en . live.
  43. ftp://pi.super-computing.org/README.our_latest_record_206b
  44. Web site: Record for pi : 206 billion decimal digits . 2022-08-04 . www.cecm.sfu.ca.
  45. Web site: Archived copy . 2010-07-08 . https://web.archive.org/web/20110312035524/http://www.super-computing.org/pi_current.html . 2011-03-12 . dead .
  46. Web site: Archived copy . 2009-08-18 . https://web.archive.org/web/20090823020534/http://www.hpcs.is.tsukuba.ac.jp/~daisuke/pi.html . 2009-08-23 . dead .
  47. Web site: Bellard . Fabrice . Fabrice Bellard . Computation of 2700 billion decimal digits of Pi using a Desktop Computer . 11 Feb 2010 . 4th revision . en . 12242318.
  48. Web site: PI-world. calico.jp. 28 August 2015. https://web.archive.org/web/20150831180053/http://piworld.calico.jp/estart.html. 31 August 2015. dead.
  49. Web site: y-cruncher – A Multi-Threaded Pi Program. numberworld.org. 28 August 2015.
  50. Web site: Pi – 5 Trillion Digits. numberworld.org. 28 August 2015.
  51. Web site: Pi – 10 Trillion Digits. numberworld.org. 28 August 2015.
  52. Web site: Pi – 12.1 Trillion Digits. numberworld.org. 28 August 2015.
  53. Web site: Pi: Notable large computations . numberworld.org . 16 March 2024.
  54. Web site: pi2e. pi2e.ch. 15 November 2016.
  55. Web site: Pi: Notable large computations . numberworld.org . 16 March 2024.
  56. Web site: Hexadecimal Digits are Correct! – pi2e trillion digits of pi. pi2e.ch. 31 October 2016. 15 November 2016.
  57. Web site: Google Cloud Topples the Pi Record. 14 March 2019.
  58. Web site: The Pi Record Returns to the Personal Computer. 30 January 2020.
  59. Web site: Calculating Pi: My attempt at breaking the Pi World Record. 26 June 2019. 30 January 2020.
  60. Web site: 2021-08-14. Pi-Challenge - world record attempt by UAS Grisons - University of Applied Sciences of the Grisons. dead. 2021-08-17. www.fhgr.ch. https://web.archive.org/web/20210817040515/https://www.fhgr.ch/en/specialist-areas/applied-future-technologies/davis-centre/pi-challenge/ . 2021-08-17 .
  61. Web site: 2021-08-16. Die FH Graubünden kennt Pi am genauesten – Weltrekord! - News - FH Graubünden. live. 2021-08-17. www.fhgr.ch. de. https://web.archive.org/web/20210817060326/https://www.fhgr.ch/news/newsdetail/die-fh-graubuenden-kennt-pi-am-genauesten-weltrekord/ . 2021-08-17 .
  62. Web site: Calculating 100 trillion digits of pi on Google Cloud . 2022-06-10 . Google Cloud Blog . en.
  63. Web site: 100 Trillion Digits of Pi . 2022-06-10 . numberworld.org.
  64. Web site: StorageReview Calculated 100 Trillion Digits of Pi in 54 days, Besting Google Cloud . 2023-12-02 . storagereview.com . en.
  65. Web site: The Need for Speed! . 19 April 2023 . 2023-12-25 . numberworld.org.
  66. Web site: Ranous . Jordan . 2024-03-13 . 105 Trillion Pi Digits: The Journey to a New Pi Calculation Record . 2024-03-14 . StorageReview.com . en-US.
  67. Web site: Alexander J. . Yee . 2024-03-14 . Limping to a new Pi Record of 105 Trillion Digits . NumberWorld.org . 2024-03-16.
  68. Web site: Ranous . Jordan . 2024-06-28 . StorageReview Lab Breaks Pi Calculation World Record with Over 202 Trillion Digits . 2024-07-02 . StorageReview.com . en-US.
  69. Web site: Alexander J. . Yee . 2024-06-28 . Pi Record Smashed at 202 Trillion Digits . NumberWorld.org . 2024-06-30.