Golden Ratio

Decimal Digits: 1,000,000,000,000

Hexadecimal Digits: 830,482,023,722

By Alexander J. Yee

(Last updated: August 17, 2015)

 

 

Notable Large Computations:

Here is a list of notable large computations that have been done using either y-cruncher or by applications using the YMP library.

Date Completed: Who: Decimal Digits: Compute Time: Computer: Comments:
July 22, 2015
July 23, 2015
Ron Watkins
Dustin Kirkland
2,000,000,000,000

Compute:  77.3 hours

Verify:  76.33 hours

Compute:  79.3 hours

Verify:  80.8 hours

4 x Xeon X6550 @ 2 GHz - 512 GB
Xeon E5-2676 v3 @ 2.4 GHz - 64 GB
World Record Size Computation
July 8, 2010 Alexander Yee 1,000,000,000,000

Compute:  114 hours (4.7 days)
Verify:  ~7 days*
*Not in a continuous run.

"Nagisa"
2 x Intel Xeon X5482 @ 3.2 GHz
64 GB DDR2 FB-DIMM
1.5 TB (Boot + Output)
4 x 1 TB (2 x 2 RAID0) + 6 x 2 TB
Burn-In Test for New Hardware
World Record Size Computation

But the digits were deleted
shortly after the computation.
June 27, 2010 Alexander Yee 100,000,000,000

Compute:  4.3 hours (6.1 hours total)

Burn-In Test for New Hardware

 

Selected Digits:

Below a list of selected digits. These can be used to verify your own computations.

1.
1.
6180339887 4989484820 4586834365 6381177203 0917980576 : 50
2862135448 6227052604 6281890244 9707207204 1893911374 : 100
9e3779b97f 4a7c15f39c c0605cedc8 341082276b f3a27251f8 : 50
6c6a11d0c1 8e952767f0 b153d27b7f 0347045b5b f1827f0188 : 100
6207995663 8801786185 5915944111 7250923132 7977113803 : 10,000
7681152452 1744973961 3674882204 6480519688 7543419695 : 12,000
6370022120 3275243899 9773600607 4042702972 2036347780 : 15,000
0456594474 3335678316 7270372963 6367594216 9993795216 : 20,000
5503138776 3911931672 0661902999 2444351317 6141601484 : 25,000
9138052922 8298148024 3291527099 4853499367 9984468736 : 40,000
7262760054 3738535562 8686571735 8459635123 7742461705 : 50,000
4954920484 8061994277 9316725614 9877162981 4481115789 : 75,000
c5587e8b45 c7f61a4257 402e174cf8 1e5faa9812 0d48cba6ea : 10,000
51de1ba464 da62e09e82 c8a0e977b3 aafa3777bc 1d31838d0d : 12,000
18bda3f630 9be4c9b5d4 ee9d498eca 846dc28ed5 c22487aa7d : 15,000
447fc487c5 65d650be1b 0059bd7b95 becb66f269 565c8559d8 : 20,000
56c9f3861b 045dc21713 da62fb90f7 521e7af2e5 192a0c383a : 25,000
6f91ba041f 7c130dd01f 6e3f308c8b cc89767bd6 ceeaf4462c : 40,000
9d4296072f 3fcd341f59 a485864b17 8aa0e01ad8 d2b11d4a1b : 50,000
ce2858c04e 1e7f64b5b8 35bd8c6cc4 585b877184 cb2d505834 : 75,000
2734491784 6772669409 1708248769 7883673974 9559326106 : 100,000
6953970075 3273009244 7590045407 2202847416 2908784797 : 120,000
8313151106 0806773429 9476880974 4898637053 3616572464 : 150,000
4809921346 3533683026 1661229791 7762250650 0116023389 : 200,000
7840291704 7232138377 4625416325 0395907906 6115475872 : 250,000
5229700153 0367083634 9584648717 0220219828 2077909238 : 400,000
7412778371 9236800941 7580998479 1387666578 8000214671 : 500,000
2240134511 1909225970 2381249555 0072404760 4505098760 : 750,000
c9a1762f42 5b1f7cf620 8fbcbe0595 c576f3ed49 cce5c9e44c : 100,000
e008df0007 7fc7a0864a 6d84547ce6 9edb29d996 5b068c9552 : 120,000
0d5ca79b92 7d274584e5 61be044ff5 d84a09d0cd 6ab2ecd212 : 150,000
f775289b95 2889191a55 94a6b34607 c053b241c8 d90ab3c7e3 : 200,000
df64fc4585 f31a451586 d7d95abfb3 da43be5212 73135d38fc : 250,000
d605ab6307 d2dfe3df8f f4c62dda82 0f43b54566 336532608c : 400,000
1366197b92 9cb2f560c4 7c7c3282d4 8590e41d16 3150c107f1 : 500,000
cb64b933a1 b09cf1fff4 e2e7481330 12d70c05a7 ad1f891d7c : 750,000
7594202182 9737743512 5197077601 3387228787 4153226344 : 1,000,000
8997716692 3908091141 6209119981 6360522174 4375522776 : 1,200,000
4305877155 4295023142 6060934029 3504287199 7401011881 : 1,500,000
8775349876 1122491683 6952948394 9521345297 0240073307 : 2,000,000
1124174310 2688834674 3272648470 3825821636 6848098732 : 2,500,000
6622525475 5233092406 9584254124 6910188796 7193368569 : 4,000,000
0378381495 8810591774 5254885358 3899571100 0973082960 : 5,000,000
7887717576 8633331996 4930938891 2985076383 4101214274 : 7,500,000
352292c178 d95c07cd3d fcd7080892 4f6065250e cdf514fb03 : 1,000,000
05c469a165 312dadb527 2555daad44 e48d0146fa 0e2dafeb30 : 1,200,000
ddfc1a660d 2e856fcbea 51f105efab 98a9106fd6 91ea4f852f : 1,500,000
f1097478ac eea5d5dfeb 7c53605d67 d81914c4f2 f9658957bf : 2,000,000
d7b3aedb32 9deaae5473 64532df4cf 9b194fd6da 53b5174cdd : 2,500,000
0ed7774fbb 897329f62d c328c68d9c dfc3350f13 0f1f80a641 : 4,000,000
eb597af136 55b2e158b8 80d67e0097 5e92111993 f22ee4cb81 : 5,000,000
51bba2b4fd bd40021737 37c5f228c5 3368aa1b65 3ca6d6abad : 7,500,000
4586050538 3757681216 8794894735 6210004401 4825797564 : 10,000,000
5648627310 8261010563 9044213535 2539742126 2737402066 : 12,000,000
9395309326 8868570301 1818329134 9072397646 6484465601 : 15,000,000
7965541626 6865653261 2023386313 7837119503 1194470092 : 20,000,000
9375364293 7471487272 7492297634 1846278533 7395898296 : 25,000,000
7267427657 6118787849 6556307535 9002817224 0638106165 : 40,000,000
1347464498 2814847716 2605838749 0070073877 6464917652 : 50,000,000
2688772820 8372630153 7112814401 2354007377 0560695110 : 75,000,000
522fc31979 bd5cd63410 8b2b5874bd e5b5ef8982 cf077f5dc9 : 10,000,000
a9fa38e5e0 078db1a3e1 8002293e20 bb7c18a879 4b3c72f22e : 12,000,000
387312abf7 46bb1b606f 8e653e6c6e 4d1a2aa73d 7fb5714cdb : 15,000,000
52e9f1ed70 2fb9dd6e45 662c5098b4 36a4420e49 954abd2bd7 : 20,000,000
cdbcd3de8f e72c1561aa f87c338b76 256bc2950f 0ae15b8f94 : 25,000,000
2afde0bee7 d770c56b4a f1df06cc5d 969d44aad8 8b49295d33 : 40,000,000
b07601aaaa b935ad7071 c9d50618e7 25c0a8e99f c1307e3c6d : 50,000,000
702e22d38c ed6c5b7f3d 975ae48889 fd7ce968d5 dd79492b99 : 75,000,000
4186130718 6909500836 2519505480 1837059131 8941970031 : 100,000,000
7347780649 4553403567 8912332646 4505162733 3483893958 : 120,000,000
2425389603 8970657298 5604388325 4781661080 5031277699 : 150,000,000
9001301839 6535661965 8866912567 4285363871 5220550228 : 200,000,000
8770259966 1178348554 1920818701 3368919537 4895160385 : 250,000,000
4719970409 3878272539 8522103926 9027336022 0520656588 : 400,000,000
6884146690 5791140710 9585034650 0772388124 9666797539 : 500,000,000
6798003782 2762031039 0979733957 7457245262 4241215380 : 750,000,000
80b4de04f0 46defdaae0 309eb60083 d7148d239d 38602c4d81 : 100,000,000
24d7548dcc 1d79abc631 ebd3bc164f 7403c6309b e8abb8a7d8 : 120,000,000
9a72e26771 8451c20b41 ef87dff74b 59272b342f bfc4a6e26c : 150,000,000
c639d9f438 328e47dff7 8eb1702098 c7b5bf8dd5 f2de35936e : 200,000,000
2ff147cfda 9dd3d1deb8 9a4247f2bd 2c72c4805e cbb97f855a : 250,000,000
299bec4bbc f4e1deffed 52827b8e0e 2487cc1037 b13472ee06 : 400,000,000
f68dff3ef2 f63e565574 fefe412700 953744605e 35bac4436d : 500,000,000
8f375dc3bf e43a263436 b7534a18d1 385ba90fb9 b462f23415 : 750,000,000
5997155517 4454738380 6284019434 1530262587 3891332833 : 1,000,000,000
6368500071 6707748255 6285593850 8264655320 1888765828 : 1,200,000,000
5558340438 3412454734 7006848135 3506716409 1827231489 : 1,500,000,000
0450639677 2012797682 8973004842 8806302385 7406873819 : 2,000,000,000
0530503036 7110853168 2009254889 5751634610 5783977108 : 2,500,000,000
4933272796 3264996293 0068673206 3867319963 5656696935 : 4,000,000,000
1642076415 1471697644 4495847980 4736378983 3399537060 : 5,000,000,000
6299651140 2257441696 9607186728 2216779445 2317176147 : 7,500,000,000
621a7e4a58 9295d75323 3623b96db2 6218286224 1adc9df049 : 1,000,000,000
2c0c86e40f 6b34c1a337 56f97124c3 2a955216e0 dcca7e00e4 : 1,200,000,000
7277ba03ad a5d82b11c5 60e4b228b4 07d75bbdc5 ad7c9bb91d : 1,500,000,000
cc37991223 ed9d9664fa 1a2005d8a2 7b626b27d7 e6cd68ef53 : 2,000,000,000
c9cf1b9b8e d40db735c9 9c6a84a6fa 9f115ed0aa 607b90dc8e : 2,500,000,000
6df81d388e 6da53536af ab4da8e7db 7be85b8603 9a52e0898d : 4,000,000,000
18adc6e30b 12a9f1d4a7 1ed898c9a1 183590b3da 7f85a07c9b : 5,000,000,000
4474d76883 bda1a66d46 26a17cdc7f f4a073e58f 480f53960f : 7,500,000,000
4643236373 7662543421 0515442930 4312640839 3761355984 : 10,000,000,000
0812069347 7047077344 5335828642 3068874737 5288179566 : 12,000,000,000
6608923688 2091274089 3997811450 0689326336 4972118837 : 15,000,000,000
7246331384 5533605523 4909008336 7933986523 7886434206 : 20,000,000,000
8441404858 0755243310 6389683605 4809510515 4851784530 : 25,000,000,000
5443527806 1016923003 3552122001 6367549620 0370219421 : 40,000,000,000
7700229052 5827171817 6519840546 7111759357 5690744542 : 50,000,000,000
6723312199 0897633511 4929117516 0771270939 2767287610 : 75,000,000,000
f7123c7adc e52b22647c 0324dc1dd0 18846ce9f0 bfb3dfe556 : 10,000,000,000
f3378af541 9a090043b0 a81816ce92 0aabbd45a2 6f047ed504 : 12,000,000,000
84654a3464 7c5722f041 9af05e8108 7de531ac2a bc56b6f1d4 : 15,000,000,000
0ca731ff61 6d8895e443 b9d850d3cd ce8476dc51 05a57030c1 : 20,000,000,000
32cf240dd3 65314044b0 3dfabe58e2 6281e8c85c db18b547e9 : 25,000,000,000
f07293c8cb 95ef43f1ed 587eeed908 2d28eba511 76080af981 : 40,000,000,000
31afde1954 cab49e09e5 38eb304f81 cd259cbdd2 c029b962c5 : 50,000,000,000
eb5aaa9e1e 1a9119e991 ba0ccec523 42bf5fdbcc 869f0ceeac : 75,000,000,000
0739037835 9306874429 0190694389 1707692248 6968748049 : 100,000,000,000
2866504985 7814879096 4581898701 4567230466 4915646067 : 120,000,000,000
6788537469 6104328295 6311439126 9730806081 5519781619 : 150,000,000,000
4848977133 7075807173 3831815885 7425067411 4775622374 : 200,000,000,000
3018530037 7765598817 7460233769 9588038415 5161548200 : 250,000,000,000
9137986630 2889935825 5089010823 5140880600 2335642277 : 400,000,000,000
5611239323 9230834328 3884669705 5420835622 0825922738 : 500,000,000,000
9131615397 7713403991 2483922299 0078590288 3311055318 : 750,000,000,000
19a8969e2e 584e11e0a2 b00c4fc7a2 136f13794d f5041a746d : 100,000,000,000
a3ca976958 d7693df65b 9e0559101d 6e77b83f74 5a1f5d875a : 120,000,000,000
0a57e600d7 54d0922c45 30ded9ce61 a48d2e61c6 0cfb3e19b2 : 150,000,000,000
5c3083dc2c 077a4c58d9 093c440a7f 2127e70b44 8904075c1f : 200,000,000,000
2fb760826b 9a7a6c634b b03fda0b8b 1ad4907704 e5b6611460 : 250,000,000,000
382cb2b185 5e473cdd59 1419f51859 c4399a059e 4c07406f28 : 400,000,000,000
9201a0374d 47ddbbbcd8 5bdd1e728d c805f7b114 d4e5ed5283 : 500,000,000,000
20938120a0 3af6a174ab 5865b70bf6 0985ec456e 19943a0f31 : 750,000,000,000
5428986734 6535846589 3743851405 1102915224 5896454442 : 1,000,000,000,000
01b78d9009 d968733d97 5ecdec94ef e9c690e9c9 ab93150c12 : 830,482,023,700
2308c6ccd3 63c03f1994 be

 

Digit Statistics:

 

Download Digits:

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Questions or Comments

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