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Chronology of computation of π

May 15, 2023

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

The last 100 decimal digits[1] of the latest 2022 world record computation are:[2]

 4658718895 1242883556 4671544483 9873493812 1206904813 2656719174 5255431487 2142102057 7077336434 3095295560
Graph showing how the record precision of numerical approximations to pi measured in decimal places (depicted on a logarithmic scale), evolved in human history. The time before 1400 is compressed.

Before 1400

Date Who Description/Computation method used Value Decimal places
(world records
in bold)
2000? BCЕ Ancient Egyptians[3] 4 × (8⁄9)2 3.1605... 1
2000? BCЕ Ancient Babylonians[3] 3 + 1⁄8 3.125 1
2000? BCЕ Ancient Sumerians[4] 3 + 23/216 3.1065 1
1200? BCЕ Ancient Chinese[3] 3 3 0
800–600 BCE Shatapatha Brahmana – 7.1.1.18 [5] 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."[6]

25⁄8 = 3.125 1
800? BCЕ Shulba Sutras[7]

[8][9]

 (6⁄(2 + √2))2 3.088311 ... 0
550? BCЕ Bible (1 Kings 7:23)[3] "...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" 3 0
434 BCE Anaxagoras attempted to square the circle[10] compass and straightedge Anaxagoras didn't offer any solution 0
400 BCE to 400 CE Vyasa[11]

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.
..."

3 0
c. 250 BCE Archimedes[3] 223⁄71 < π < 22⁄7 3.140845... < π < 3.142857... 2
15 BCE Vitruvius[8] 25⁄8 3.125 1
between 1 and 5 Liu Xin[8][12][13] Unknown method giving a figure for a jialiang which implies a value for π π ≈ 162⁄(√50+0.095)2. 3.1547... 1
130 Zhang Heng (Book of the Later Han)[3] √10 = 3.162277...
736⁄232 		3.1622... 1
150 Ptolemy[3] 377⁄120 3.141666... 3
250 Wang Fan[3] 142⁄45 3.155555... 1
263 Liu Hui[3] 3.141024 < π < 3.142074
3927⁄1250 		3.1416 3
400 He Chengtian[8] 111035⁄35329 3.142885... 2
480 Zu Chongzhi[3] 3.1415926 < π < 3.1415927
355⁄113 		3.1415926 7
499 Aryabhata[3] 62832⁄20000 3.1416 3
640 Brahmagupta[3] √10 3.162277... 1
800 Al Khwarizmi[3] 3.1416 3
1150 Bhāskara II[8] 3927⁄1250 and 754⁄240 3.1416 3
1220 Fibonacci[3] 3.141818 3
1320 Zhao Youqin[8] 3.141592 6

1400–1949

Date Who Note Decimal places
(world records in bold)
All records from 1400 onwards are given as the number of correct decimal places.
1400 Madhava of Sangamagrama Discovered the infinite power series expansion of π,
now known as the Leibniz formula for pi[14]		 10
1424 Jamshīd al-Kāshī[15] 16
1573 Valentinus Otho 355⁄113 6
1579 François Viète[16] 9
1593 Adriaan van Roomen[17] 15
1596 Ludolph van Ceulen 20
1615 32
1621 Willebrord Snell (Snellius) Pupil of Van Ceulen 35
1630 Christoph Grienberger[18][19] 38
1654 Christiaan Huygens Used a geometrical method equivalent to Richardson extrapolation 10
1665 Isaac Newton[3] 16
1681 Takakazu Seki[20] 11
16
1699 Abraham Sharp[3] Calculated pi to 72 digits, but not all were correct 71
1706 John Machin[3] 100
1706 William Jones Introduced the Greek letter 'π'
1719 Thomas Fantet de Lagny[3] Calculated 127 decimal places, but not all were correct 112
1722 Toshikiyo Kamata 24
1722 Katahiro Takebe 41
1739 Yoshisuke Matsunaga 51
1748 Leonhard Euler Used the Greek letter 'π' in his book Introductio in Analysin Infinitorum and assured its popularity.
1761 Johann Heinrich Lambert Proved that π is irrational
1775 Euler Pointed out the possibility that π might be transcendental
1789 Jurij Vega[21] Calculated 140 decimal places, but not all were correct 126
1794 Adrien-Marie Legendre Showed that π2 (and hence π) is irrational, and mentioned the possibility that π might be transcendental.
Late 18th century Anonymous manuscript Turns up at Radcliffe Library, in Oxford, England, discovered by F. X. von Zach, giving the value of pi to 154 digits, 152 of which were correct[22] 152
1824 William Rutherford[3] Calculated 208 decimal places, but not all were correct 152
1844 Zacharias Dase and Strassnitzky[3] Calculated 205 decimal places, but not all were correct 200
1847 Thomas Clausen[3] Calculated 250 decimal places, but not all were correct 248
1853 Lehmann[3] 261
1853 Rutherford[3] 440
1853 William Shanks[23] 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 incorrect (the error was found by D. F. Ferguson in 1946). 527
1882 Ferdinand von Lindemann Proved that π is transcendental (the Lindemann–Weierstrass theorem)
1897 The U.S. state of Indiana Came close to legislating the value 3.2 (among others) for π. 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.[24] 0
1910 Srinivasa Ramanujan Found several rapidly converging infinite series of π, which can compute 8 decimal places of π 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 π.
1946 D. F. Ferguson Most digits ever calculated by hand. 620
1947 Ivan Niven Gave a very elementary proof that π is irrational
January 1947 D. F. Ferguson Made use of a desk calculator 710
September 1947 D. F. Ferguson Desk calculator 808
1949 Levi B. Smith and John Wrench Made use of a desk calculator 1,120

1949–2009

Date Who Implementation Time Decimal places
(world records in bold)
All records from 1949 onwards were calculated with electronic computers.
1949 G. W. Reitwiesner et al. The first to use an electronic computer (the ENIAC) to calculate π [25] 70 hours 2,037
1953 Kurt Mahler Showed that π is not a Liouville number
1954 S. C. Nicholson & J. Jeenel Using the NORC[26] 13 minutes 3,093
1957 George E. Felton Ferranti Pegasus computer (London), calculated 10,021 digits, but not all were correct[27][28] 33 hours 7,480
January 1958 Francois Genuys IBM 704[29] 1.7 hours 10,000
May 1958 George E. Felton Pegasus computer (London) 33 hours 10,021
1959 Francois Genuys IBM 704 (Paris)[30] 4.3 hours 16,167
1961 Daniel Shanks and John Wrench IBM 7090 (New York)[31] 8.7 hours 100,265
1961 J.M. Gerard IBM 7090 (London) 39 minutes 20,000
1966 Jean Guilloud and J. Filliatre IBM 7030 (Paris) 28 hours[failed verification] 250,000
1967 Jean Guilloud and M. Dichampt CDC 6600 (Paris) 28 hours 500,000
1973 Jean Guilloud and Martine Bouyer CDC 7600 23.3 hours 1,001,250
1981 Kazunori Miyoshi and Yasumasa Kanada FACOM M-200[28] 137.3 hours 2,000,036
1981 Jean Guilloud Not known 2,000,050
1982 Yoshiaki Tamura MELCOM 900II[28] 7.23 hours 2,097,144
1982 Yoshiaki Tamura and Yasumasa Kanada HITAC M-280H[28] 2.9 hours 4,194,288
1982 Yoshiaki Tamura and Yasumasa Kanada HITAC M-280H[28] 6.86 hours 8,388,576
1983 Yasumasa Kanada, Sayaka Yoshino and Yoshiaki Tamura HITAC M-280H 16,777,206
October 1983 Yasunori Ushiro and Yasumasa Kanada HITAC S-810/20 10,013,395
October 1985 Bill Gosper Symbolics 3670 17,526,200
January 1986 David H. Bailey CRAY-2 29,360,111
September 1986 Yasumasa Kanada, Yoshiaki Tamura HITAC S-810/20 33,554,414
October 1986 Yasumasa Kanada, Yoshiaki Tamura HITAC S-810/20 67,108,839
January 1987 Yasumasa Kanada, Yoshiaki Tamura, Yoshinobu Kubo and others NEC SX-2 134,214,700
January 1988 Yasumasa Kanada and Yoshiaki Tamura HITAC S-820/80[32] 5.95 hours 201,326,551
May 1989 Gregory V. Chudnovsky & David V. Chudnovsky CRAY-2 & IBM 3090/VF 480,000,000
June 1989 Gregory V. Chudnovsky & David V. Chudnovsky IBM 3090 535,339,270
July 1989 Yasumasa Kanada and Yoshiaki Tamura HITAC S-820/80 536,870,898
August 1989 Gregory V. Chudnovsky & David V. Chudnovsky IBM 3090 1,011,196,691
19 November 1989 Yasumasa Kanada and Yoshiaki Tamura HITAC S-820/80[33] 1,073,740,799
August 1991 Gregory V. Chudnovsky & David V. Chudnovsky Homemade parallel computer (details unknown, not verified) [34][33] 2,260,000,000
18 May 1994 Gregory V. Chudnovsky & David V. Chudnovsky New homemade parallel computer (details unknown, not verified) 4,044,000,000
26 June 1995 Yasumasa Kanada and Daisuke Takahashi HITAC S-3800/480 (dual CPU) [35] 3,221,220,000
1995 Simon Plouffe Finds a formula that allows the nth hexadecimal digit of pi to be calculated without calculating the preceding digits.
28 August 1995 Yasumasa Kanada and Daisuke Takahashi HITAC S-3800/480 (dual CPU) [36][37] 56.74 hours? 4,294,960,000
11 October 1995 Yasumasa Kanada and Daisuke Takahashi HITAC S-3800/480 (dual CPU) [38][37] 116.63 hours 6,442,450,000
6 July 1997 Yasumasa Kanada and Daisuke Takahashi HITACHI SR2201 (1024 CPU) [39][40] 29.05 hours 51,539,600,000
5 April 1999 Yasumasa Kanada and Daisuke Takahashi HITACHI SR8000 (64 of 128 nodes) [41][42] 32.9 hours 68,719,470,000
20 September 1999 Yasumasa Kanada and Daisuke Takahashi HITACHI SR8000/MPP (128 nodes) [43][44] 37.35 hours 206,158,430,000
24 November 2002 Yasumasa Kanada & 9 man team HITACHI SR8000/MPP (64 nodes), Department of Information Science at the University of Tokyo in Tokyo, Japan[45] 600 hours 1,241,100,000,000
29 April 2009 Daisuke 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 hours 2,576,980,377,524

2009–present

Date Who Implementation Time Decimal places
(world records in bold)
All records from Dec 2009 onwards are calculated and verified on servers and/or home computers with commercially available parts.
31 December 2009 Fabrice Bellard
  • 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: 103 days
  • Verification of the binary digits: 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, Chudnovsky algorithm, see [47] for Bellard's homepage.[48]
 131 days 2,699,999,990,000
2 August 2010 Shigeru Kondo[49]
  • using y-cruncher[50] by Alexander Yee
  • the Chudnovsky algorithm was used for main computation
  • verification used the Bellard & BBP (Plouffe) formulas on different computers; both computed 32 hexadecimal digits ending with the 4,152,410,118,610th.
  • 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 (primary), 66 hours (secondary)
  • Verification of the binary digits were done simultaneously on two separate computers during the main computation.[51]
 90 days 5,000,000,000,000
17 October 2011 Shigeru Kondo[52]
  • using y-cruncher by Alexander Yee
  • the Chudnovsky algorithm was used for main computation
  • Verification using the Bellard & BBP (Plouffe) formulas: 1.86 days and 4.94 days
 371 days 10,000,000,000,050
28 December 2013 Shigeru Kondo[53]
  • using y-cruncher 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
  • the Chudnovsky algorithm was used for main computation
  • Verification using Bellard's variant of the BBP formula: 46 hours
 94 days 12,100,000,000,050
8 October 2014 Sandon Nash Van Ness "houkouonchi"[54]
  • using y-cruncher by Alexander Yee
  • with 2× Xeon E5-4650L @ 2.6 GHz
  • 192 GiB DDR3 @ 1333 MHz
  • 24× 4 TB + 30× 3 TB
  • the Chudnovsky algorithm was used for main computation
  • Verification using the BBP formula: 182 hours
 208 days 13,300,000,000,000
11 November 2016 Peter Trueb[55][56]
  • using y-cruncher by Alexander Yee
  • with 4× Xeon E7-8890 v3 @ 2.50 GHz (72 cores, 144 threads)
  • 1.25 TiB DDR4
  • 20× 6 TB
  • the Chudnovsky algorithm was used for main computation
  • Verification using Bellard's variant of the BBP formula: 28 hours[57]
 105 days 22,459,157,718,361
= ⌊πe × 1012⌋
14 March 2019 Emma Haruka Iwao[58]
  • using y-cruncher v0.7.6
  • Computation: 1× n1-megamem-96 (96 vCPU, 1.4TB) with 30TB of SSD
  • Storage: 24× n1-standard-16 (16 vCPU, 60GB) with 10TB of SSD
  • the Chudnovsky algorithm was used for main computation
  • Verification: 20 hours using Bellard's 7-term BBP formula, and 28 hours using Plouffe's 4-term BBP formula
 121 days 31,415,926,535,897
= ⌊π × 1013⌋
29 January 2020 Timothy Mullican[59][60]
  • using y-cruncher v0.7.7
  • Computation: 4x Intel Xeon CPU E7-4880 v2 @ 2.50 GHz
  • 320GB DDR3 PC3-8500R ECC RAM
  • 48× 6TB HDDs (Computation) + 47× LTO Ultrium 5 1.5TB Tapes (Checkpoint Backups) + 12× 4TB HDDs (Digit Storage)
  • the Chudnovsky algorithm was used for main computation
  • Verification: 17 hours using Bellard's 7-term BBP formula, 24 hours using Plouffe's 4-term BBP formula
 303 days 50,000,000,000,000
14 August 2021 Team DAViS of the University of Applied Sciences of the Grisons[61][62]
  • using y-cruncher v0.7.8
  • Computation: AMD Epyc 7542 @ 2.9 GHz
  • 1 TiB of memory
  • 38x 16 TB HDDs (Of those, 34 are used for swapping and 4 used for storage)
  • the Chudnovsky algorithm was used for main computation
  • Verification: 34 hours using Bellard's 4-term BBP formula
 108 days 62,831,853,071,796
= ⌊2π × 1013⌋
21 March 2022 Emma Haruka Iwao[63][64]
  • using y-cruncher v0.7.8
  • Computation: n2-highmem-128 (128 vCPU and 864 GB RAM)
  • Storage: 663 TB
  • the Chudnovsky algorithm was used for main computation
  • Verification: 12.6 hours using BBP formula
 158 days 100,000,000,000,000

See also

References

  1. ^ The last digit shown here is the 100,000,000,000,000th digit of π.
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  4. ^ "Origins: 3.14159265…". Biblical Archaeology Society. 2022-03-14. Retrieved 2022-06-08.
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    Sandifer, Ed (2006). (PDF). Southern Connecticut State University. Archived from the original (PDF) on 2012-02-04.
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  62. ^ "Die FH Graubünden kennt Pi am genauesten – Weltrekord! - News - FH Graubünden". www.fhgr.ch (in German). 2021-08-16. from the original on 2021-08-17. Retrieved 2021-08-17.
  63. ^ "Calculating 100 trillion digits of pi on Google Cloud". Google Cloud Blog. Retrieved 2022-06-10.
  64. ^ "News (2019)". numberworld.org. Retrieved 2022-06-10.

External links

  • Borwein, Jonathan, "The Life of Pi"
  • Stu's Pi page

May 15, 2023
chronology, computation, this, article, needs, additional, citations, verification, please, help, improve, this, article, adding, citations, reliable, sources, unsourced, material, challenged, removed, find, sources, news, newspapers, books, scholar, jstor, oc. This article needs additional citations for verification Please help improve this article by adding citations to reliable sources Unsourced material may be challenged and removed Find sources Chronology of computation of p news newspapers books scholar JSTOR October 2014 Learn how and when to remove this template message The table below is a brief chronology of computed numerical values of or bounds on the mathematical constant pi p For more detailed explanations for some of these calculations see Approximations of p The last 100 decimal digits 1 of the latest 2022 world record computation are 2 4658718895 1242883556 4671544483 9873493812 1206904813 2656719174 5255431487 2142102057 7077336434 3095295560 Contents 1 Before 1400 2 1400 1949 3 1949 2009 4 2009 present 5 See also 6 References 7 External links Graph showing how the record precision of numerical approximations to pi measured in decimal places depicted on a logarithmic scale evolved in human history The time before 1400 is compressed Before 1400 EditDate Who Description Computation method used Value Decimal places world records in bold 2000 BCE Ancient Egyptians 3 4 8 9 2 3 1605 12000 BCE Ancient Babylonians 3 3 1 8 3 125 12000 BCE Ancient Sumerians 4 3 23 216 3 1065 11200 BCE Ancient Chinese 3 3 3 0800 600 BCE Shatapatha Brahmana 7 1 1 18 5 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 6 25 8 3 125 1800 BCE Shulba Sutras 7 8 9 6 2 2 2 3 088311 0550 BCE Bible 1 Kings 7 23 3 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 3 0434 BCE Anaxagoras attempted to square the circle 10 compass and straightedge Anaxagoras didn t offer any solution 0400 BCE to 400 CE Vyasa 11 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 3 0c 250 BCE Archimedes 3 223 71 lt p lt 22 7 3 140845 lt p lt 3 142857 215 BCE Vitruvius 8 25 8 3 125 1between 1 and 5 Liu Xin 8 12 13 Unknown method giving a figure for a jialiang which implies a value for p p 162 50 0 095 2 3 1547 1130 Zhang Heng Book of the Later Han 3 10 3 162277 736 232 3 1622 1150 Ptolemy 3 377 120 3 141666 3250 Wang Fan 3 142 45 3 155555 1263 Liu Hui 3 3 141024 lt p lt 3 1420743927 1250 3 1416 3400 He Chengtian 8 111035 35329 3 142885 2480 Zu Chongzhi 3 3 1415926 lt p lt 3 1415927 355 113 3 1415926 7499 Aryabhata 3 62832 20000 3 1416 3640 Brahmagupta 3 10 3 162277 1800 Al Khwarizmi 3 3 1416 31150 Bhaskara II 8 3927 1250 and 754 240 3 1416 31220 Fibonacci 3 3 141818 31320 Zhao Youqin 8 3 141592 61400 1949 EditDate Who Note Decimal places world records in bold All records from 1400 onwards are given as the number of correct decimal places 1400 Madhava of Sangamagrama Discovered the infinite power series expansion of p now known as the Leibniz formula for pi 14 101424 Jamshid al Kashi 15 161573 Valentinus Otho 355 113 61579 Francois Viete 16 91593 Adriaan van Roomen 17 151596 Ludolph van Ceulen 201615 321621 Willebrord Snell Snellius Pupil of Van Ceulen 351630 Christoph Grienberger 18 19 381654 Christiaan Huygens Used a geometrical method equivalent to Richardson extrapolation 101665 Isaac Newton 3 161681 Takakazu Seki 20 11 161699 Abraham Sharp 3 Calculated pi to 72 digits but not all were correct 711706 John Machin 3 1001706 William Jones Introduced the Greek letter p 1719 Thomas Fantet de Lagny 3 Calculated 127 decimal places but not all were correct 1121722 Toshikiyo Kamata 241722 Katahiro Takebe 411739 Yoshisuke Matsunaga 511748 Leonhard Euler Used the Greek letter p in his book Introductio in Analysin Infinitorum and assured its popularity 1761 Johann Heinrich Lambert Proved that p is irrational1775 Euler Pointed out the possibility that p might be transcendental1789 Jurij Vega 21 Calculated 140 decimal places but not all were correct 1261794 Adrien Marie Legendre Showed that p 2 and hence p is irrational and mentioned the possibility that p might be transcendental Late 18th century Anonymous manuscript Turns up at Radcliffe Library in Oxford England discovered by F X von Zach giving the value of pi to 154 digits 152 of which were correct 22 1521824 William Rutherford 3 Calculated 208 decimal places but not all were correct 1521844 Zacharias Dase and Strassnitzky 3 Calculated 205 decimal places but not all were correct 2001847 Thomas Clausen 3 Calculated 250 decimal places but not all were correct 2481853 Lehmann 3 2611853 Rutherford 3 4401853 William Shanks 23 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 incorrect the error was found by D F Ferguson in 1946 5271882 Ferdinand von Lindemann Proved that p is transcendental the Lindemann Weierstrass theorem 1897 The U S state of Indiana Came close to legislating the value 3 2 among others for p 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 24 01910 Srinivasa Ramanujan Found several rapidly converging infinite series of p which can compute 8 decimal places of p 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 p 1946 D F Ferguson Most digits ever calculated by hand 6201947 Ivan Niven Gave a very elementary proof that p is irrationalJanuary 1947 D F Ferguson Made use of a desk calculator 710September 1947 D F Ferguson Desk calculator 8081949 Levi B Smith and John Wrench Made use of a desk calculator 1 1201949 2009 EditDate Who Implementation Time Decimal places world records in bold All records from 1949 onwards were calculated with electronic computers 1949 G W Reitwiesner et al The first to use an electronic computer the ENIAC to calculate p 25 70 hours 2 0371953 Kurt Mahler Showed that p is not a Liouville number1954 S C Nicholson amp J Jeenel Using the NORC 26 13 minutes 3 0931957 George E Felton Ferranti Pegasus computer London calculated 10 021 digits but not all were correct 27 28 33 hours 7 480January 1958 Francois Genuys IBM 704 29 1 7 hours 10 000May 1958 George E Felton Pegasus computer London 33 hours 10 0211959 Francois Genuys IBM 704 Paris 30 4 3 hours 16 1671961 Daniel Shanks and John Wrench IBM 7090 New York 31 8 7 hours 100 2651961 J M Gerard IBM 7090 London 39 minutes 20 0001966 Jean Guilloud and J Filliatre IBM 7030 Paris 28 hours failed verification 250 0001967 Jean Guilloud and M Dichampt CDC 6600 Paris 28 hours 500 0001973 Jean Guilloud and Martine Bouyer CDC 7600 23 3 hours 1 001 2501981 Kazunori Miyoshi and Yasumasa Kanada FACOM M 200 28 137 3 hours 2 000 0361981 Jean Guilloud Not known 2 000 0501982 Yoshiaki Tamura MELCOM 900II 28 7 23 hours 2 097 1441982 Yoshiaki Tamura and Yasumasa Kanada HITAC M 280H 28 2 9 hours 4 194 2881982 Yoshiaki Tamura and Yasumasa Kanada HITAC M 280H 28 6 86 hours 8 388 5761983 Yasumasa Kanada Sayaka Yoshino and Yoshiaki Tamura HITAC M 280H 16 777 206October 1983 Yasunori Ushiro and Yasumasa Kanada HITAC S 810 20 10 013 395October 1985 Bill Gosper Symbolics 3670 17 526 200January 1986 David H Bailey CRAY 2 29 360 111September 1986 Yasumasa Kanada Yoshiaki Tamura HITAC S 810 20 33 554 414October 1986 Yasumasa Kanada Yoshiaki Tamura HITAC S 810 20 67 108 839January 1987 Yasumasa Kanada Yoshiaki Tamura Yoshinobu Kubo and others NEC SX 2 134 214 700January 1988 Yasumasa Kanada and Yoshiaki Tamura HITAC S 820 80 32 5 95 hours 201 326 551May 1989 Gregory V Chudnovsky amp David V Chudnovsky CRAY 2 amp IBM 3090 VF 480 000 000June 1989 Gregory V Chudnovsky amp David V Chudnovsky IBM 3090 535 339 270July 1989 Yasumasa Kanada and Yoshiaki Tamura HITAC S 820 80 536 870 898August 1989 Gregory V Chudnovsky amp David V Chudnovsky IBM 3090 1 011 196 69119 November 1989 Yasumasa Kanada and Yoshiaki Tamura HITAC S 820 80 33 1 073 740 799August 1991 Gregory V Chudnovsky amp David V Chudnovsky Homemade parallel computer details unknown not verified 34 33 2 260 000 00018 May 1994 Gregory V Chudnovsky amp David V Chudnovsky New homemade parallel computer details unknown not verified 4 044 000 00026 June 1995 Yasumasa Kanada and Daisuke Takahashi HITAC S 3800 480 dual CPU 35 3 221 220 0001995 Simon Plouffe Finds a formula that allows the nth hexadecimal digit of pi to be calculated without calculating the preceding digits 28 August 1995 Yasumasa Kanada and Daisuke Takahashi HITAC S 3800 480 dual CPU 36 37 56 74 hours 4 294 960 00011 October 1995 Yasumasa Kanada and Daisuke Takahashi HITAC S 3800 480 dual CPU 38 37 116 63 hours 6 442 450 0006 July 1997 Yasumasa Kanada and Daisuke Takahashi HITACHI SR2201 1024 CPU 39 40 29 05 hours 51 539 600 0005 April 1999 Yasumasa Kanada and Daisuke Takahashi HITACHI SR8000 64 of 128 nodes 41 42 32 9 hours 68 719 470 00020 September 1999 Yasumasa Kanada and Daisuke Takahashi HITACHI SR8000 MPP 128 nodes 43 44 37 35 hours 206 158 430 00024 November 2002 Yasumasa Kanada amp 9 man team HITACHI SR8000 MPP 64 nodes Department of Information Science at the University of Tokyo in Tokyo Japan 45 600 hours 1 241 100 000 00029 April 2009 Daisuke 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 hours 2 576 980 377 5242009 present EditDate Who Implementation Time Decimal places world records in bold All records from Dec 2009 onwards are calculated and verified on servers and or home computers with commercially available parts 31 December 2009 Fabrice Bellard 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 103 days Verification of the binary digits 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 Chudnovsky algorithm see 47 for Bellard s homepage 48 131 days 2 699 999 990 0002 August 2010 Shigeru Kondo 49 using y cruncher 50 by Alexander Yee the Chudnovsky algorithm was used for main computation verification used the Bellard amp BBP Plouffe formulas on different computers both computed 32 hexadecimal digits ending with the 4 152 410 118 610th 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 primary 66 hours secondary Verification of the binary digits were done simultaneously on two separate computers during the main computation 51 90 days 5 000 000 000 00017 October 2011 Shigeru Kondo 52 using y cruncher by Alexander Yee the Chudnovsky algorithm was used for main computation Verification using the Bellard amp BBP Plouffe formulas 1 86 days and 4 94 days 371 days 10 000 000 000 05028 December 2013 Shigeru Kondo 53 using y cruncher 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 the Chudnovsky algorithm was used for main computation Verification using Bellard s variant of the BBP formula 46 hours 94 days 12 100 000 000 0508 October 2014 Sandon Nash Van Ness houkouonchi 54 using y cruncher by Alexander Yee with 2 Xeon E5 4650L 2 6 GHz 192 GiB DDR3 1333 MHz 24 4 TB 30 3 TB the Chudnovsky algorithm was used for main computation Verification using the BBP formula 182 hours 208 days 13 300 000 000 00011 November 2016 Peter Trueb 55 56 using y cruncher by Alexander Yee with 4 Xeon E7 8890 v3 2 50 GHz 72 cores 144 threads 1 25 TiB DDR4 20 6 TB the Chudnovsky algorithm was used for main computation Verification using Bellard s variant of the BBP formula 28 hours 57 105 days 22 459 157 718 361 p e 1012 14 March 2019 Emma Haruka Iwao 58 using y cruncher v0 7 6 Computation 1 n1 megamem 96 96 vCPU 1 4TB with 30TB of SSD Storage 24 n1 standard 16 16 vCPU 60GB with 10TB of SSD the Chudnovsky algorithm was used for main computation Verification 20 hours using Bellard s 7 term BBP formula and 28 hours using Plouffe s 4 term BBP formula 121 days 31 415 926 535 897 p 1013 29 January 2020 Timothy Mullican 59 60 using y cruncher v0 7 7 Computation 4x Intel Xeon CPU E7 4880 v2 2 50 GHz 320GB DDR3 PC3 8500R ECC RAM 48 6TB HDDs Computation 47 LTO Ultrium 5 1 5TB Tapes Checkpoint Backups 12 4TB HDDs Digit Storage the Chudnovsky algorithm was used for main computation Verification 17 hours using Bellard s 7 term BBP formula 24 hours using Plouffe s 4 term BBP formula 303 days 50 000 000 000 00014 August 2021 Team DAViS of the University of Applied Sciences of the Grisons 61 62 using y cruncher v0 7 8 Computation AMD Epyc 7542 2 9 GHz 1 TiB of memory 38x 16 TB HDDs Of those 34 are used for swapping and 4 used for storage the Chudnovsky algorithm was used for main computation Verification 34 hours using Bellard s 4 term BBP formula 108 days 62 831 853 071 796 2p 1013 21 March 2022 Emma Haruka Iwao 63 64 using y cruncher v0 7 8 Computation n2 highmem 128 128 vCPU and 864 GB RAM Storage 663 TB the Chudnovsky algorithm was used for main computation Verification 12 6 hours using BBP formula 158 days 100 000 000 000 000See also EditHistory of pi Approximations of pReferences Edit The last digit shown here is the 100 000 000 000 000th digit of p Validation File Retrieved 2022 06 09 a href Template Cite web html title Template Cite web cite web a CS1 maint url status link a b c d e f g h i j k l m n o p q r s t u v w David H Bailey Jonathan M Borwein Peter B Borwein Simon Plouffe 1997 The quest for pi PDF Mathematical Intelligencer 19 1 50 57 doi 10 1007 BF03024340 S2CID 14318695 Origins 3 14159265 Biblical Archaeology Society 2022 03 14 Retrieved 2022 06 08 Eggeling Julius 1882 1900 The Satapatha brahmana according to the text of the Madhyandina school Princeton Theological Seminary Library Oxford The Clarendon Press pp 302 303 a href Template Cite book html title Template Cite book cite book a CS1 maint date and year link The Sacred Books of the East The Satapatha Brahmana pt 3 Clarendon Press 1894 p 303 This article incorporates text from this source which is in the public domain 4 II Sulba Sutras www history mcs st and ac uk a b c d e f Ravi P Agarwal Hans Agarwal Syamal K Sen 2013 Birth growth and computation of pi to ten trillion digits Advances in Difference Equations 2013 100 doi 10 1186 1687 1847 2013 100 Plofker Kim 2009 Mathematics in India Princeton University Press p 18 ISBN 978 0691120676 https www math rutgers edu cherlin History Papers2000 wilson html bare URL Jadhav Dipak 2018 01 01 On The Value Implied In The Data Referred To In The Mahabharata for p Vidyottama Sanatana International Journal of Hindu Science and Religious Studies 2 1 18 doi 10 25078 ijhsrs v2i1 511 ISSN 2550 0651 S2CID 146074061 趙良五 1991 中西數學史的比較 臺灣商務印書館 ISBN 978 9570502688 via Google Books 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 Bag A K 1980 Indian Literature on Mathematics During 1400 1800 A D PDF Indian Journal of History of Science 15 1 86 p 2 827 433 388 233 9 10 11 3 14159 26535 92222 good to 10 decimal places approximated 2p to 9 sexagesimal digits Al Kashi author Adolf P Youschkevitch chief editor Boris A Rosenfeld p 256 O Connor John J Robertson Edmund F Ghiyath al Din Jamshid Mas ud al Kashi MacTutor History of Mathematics archive University of St Andrews Azarian Mohammad K 2010 Al Risala Al Muhitiyya A Summary Missouri Journal of Mathematical Sciences 22 2 64 85 doi 10 35834 mjms 1312233136 Viete Francois 1579 Canon mathematicus seu ad triangula cum adpendicibus in Latin Romanus Adrianus 1593 Ideae mathematicae pars prima sive methodus polygonorum in Latin apud Ioannem Keerbergium hdl 2027 ucm 5320258006 Grienbergerus Christophorus 1630 Elementa Trigonometrica PDF in Latin Archived from the original PDF on 2014 02 01 Hobson Ernest William 1913 Squaring the Circle a History of the Problem PDF Cambridge University Press p 27 Yoshio Mikami Eugene Smith David 2004 1914 A History of Japanese Mathematics paperback ed Dover Publications ISBN 0 486 43482 6 Vega George 1795 1789 Determination de la demi circonference d un cercle dont le diameter est 1 exprimee en 140 figures decimals Supplement Nova Acta Academiae Scientiarum Petropolitanae 11 41 44 Sandifer Ed 2006 Why 140 Digits of Pi Matter PDF Southern Connecticut State University Archived from the original PDF on 2012 02 04 Benjamin Wardhaugh Filling a Gap in the History of p An Exciting Discovery Mathematical Intelligencer 38 1 2016 6 7 Hayes Brian September 2014 Pencil Paper and Pi American Scientist Vol 102 no 5 p 342 doi 10 1511 2014 110 342 Retrieved 13 February 2022 Lopez Ortiz Alex February 20 1998 Indiana Bill sets value of Pi to 3 the news answers WWW archive Department of Information and Computing Sciences Utrecht University Archived from the original on 2005 01 09 Retrieved 2009 02 01 Reitwiesner G 1950 An ENIAC determination of p and e to more than 2000 decimal places MTAC 4 11 15 doi 10 1090 S0025 5718 1950 0037597 6 Nicholson S C Jeenel J 1955 Some comments on a NORC computation of p MTAC 9 162 164 doi 10 1090 S0025 5718 1955 0075672 5 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 p see Wrench J W Jr 1960 The evolution of extended decimal approximations to p The Mathematics Teacher 53 8 644 650 doi 10 5951 MT 53 8 0644 JSTOR 27956272 a b c d e Arndt Jorg Haenel Christoph 2001 Pi Unleashed ISBN 978 3 642 56735 3 Genuys F 1958 Dix milles decimales de p Chiffres 1 17 22 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 Shanks Daniel Wrench John W J r 1962 Calculation of p to 100 000 decimals Mathematics of Computation 16 77 76 99 doi 10 1090 S0025 5718 1962 0136051 9 Kanada Y November 1988 Vectorization of multiple precision arithmetic program and 201 326 000 decimal digits of pi calculation Supercomputing 88 Proceedings of the 1988 ACM IEEE Conference on Supercomputing Vol II Science and Applications 117 128 vol 2 doi 10 1109 SUPERC 1988 74139 ISBN 0 8186 8923 4 S2CID 122820709 a b Computers Science News 24 August 1991 Retrieved 2022 08 04 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 ftp pi super computing org README our last record 3b permanent dead link ftp pi super computing org README our last record 4b permanent dead link a b GENERAL COMPUTATIONAL UPDATE www cecm sfu ca Retrieved 2022 08 04 ftp pi super computing org README our last record 6b ftp pi super computing org README our last record 51b permanent dead link Record for pi 51 5 billion decimal digits 2005 12 24 Archived from the original on 2005 12 24 Retrieved 2022 08 04 ftp pi super computing org README our last record 68b permanent dead link https www plouffe fr simon constants Pi68billion txt bare URL plain text file ftp pi super computing org README our latest record 206b permanent dead link Record for pi 206 billion decimal digits www cecm sfu ca Retrieved 2022 08 04 Archived copy Archived from the original on 2011 03 12 Retrieved 2010 07 08 a href Template Cite web html title Template Cite web cite web a CS1 maint archived copy as title link Archived copy Archived from the original on 2009 08 23 Retrieved 2009 08 18 a href Template Cite web html title Template Cite web cite web a CS1 maint archived copy as title link Fabrice Bellard s Home Page bellard org Retrieved 28 August 2015 http bellard org pi pi2700e9 pipcrecord pdf bare URL PDF PI world calico jp Archived from the original on 31 August 2015 Retrieved 28 August 2015 y cruncher A Multi Threaded Pi Program numberworld org Retrieved 28 August 2015 Pi 5 Trillion Digits numberworld org Retrieved 28 August 2015 Pi 10 Trillion Digits numberworld org Retrieved 28 August 2015 Pi 12 1 Trillion Digits numberworld org Retrieved 28 August 2015 y cruncher A Multi Threaded Pi Program numberworld org Retrieved 14 March 2018 pi2e pi2e ch Retrieved 15 November 2016 Alexander J Yee y cruncher A Multi Threaded Pi Program numberworld org Retrieved 15 November 2016 Hexadecimal Digits are Correct pi2e trillion digits of pi pi2e ch 31 October 2016 Retrieved 15 November 2016 Google Cloud Topples the Pi Record Retrieved 14 March 2019 The Pi Record Returns to the Personal Computer Retrieved 30 January 2020 Calculating Pi My attempt at breaking the Pi World Record 26 June 2019 Retrieved 30 January 2020 Pi Challenge world record attempt by UAS Grisons University of Applied Sciences of the Grisons www fhgr ch 2021 08 14 Archived from the original on 2021 08 17 Retrieved 2021 08 17 Die FH Graubunden kennt Pi am genauesten Weltrekord News FH Graubunden www fhgr ch in German 2021 08 16 Archived from the original on 2021 08 17 Retrieved 2021 08 17 Calculating 100 trillion digits of pi on Google Cloud Google Cloud Blog Retrieved 2022 06 10 News 2019 numberworld org Retrieved 2022 06 10 External links EditBorwein Jonathan The Life of Pi Kanada Laboratory home page Stu s Pi page Takahashi s page Retrieved from https en wikipedia org w index php title Chronology of computation of p amp oldid 1152998256, wikipedia, wiki, book, books, library,

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