Statistiques de distribution de fréquence des chiffres de 0 à 9 dans Pi

Nous avons compté les occurrences et fréquences des chiffres de 0 à 9 dans les premiers 100 milliards de chiffres de pi. Nous avons constaté qu'avec l'augmentation du nombre de chiffres de pi, la fréquence des chiffres tend progressivement à être moyenne.

Dans les premiers 100 milliards de chiffres de pi, allant de moins à plus de chiffres, nous avons enregistré séparément des données sur la distribution de 82 ensembles différents de chiffres. Les nombres d'occurrences sont répertoriés ci-dessus et les fréquences sont répertoriées ci-dessous.

Table de fréquence de chaque chiffre dans les premiers 100 milliards de chiffres de Pi

# Chiffres 0 1 2 3 4 5 6 7 8 9
1 10 00.00% 220.00% 110.00% 220.00% 110.00% 220.00% 110.00% 00.00% 00.00% 110.00%
2 20 00.00% 210.00% 210.00% 420.00% 210.00% 315.00% 15.00% 15.00% 210.00% 315.00%
3 30 00.00% 26.67% 413.33% 723.33% 310.00% 310.00% 310.00% 26.67% 310.00% 310.00%
4 40 12.50% 37.50% 512.50% 717.50% 410.00% 410.00% 37.50% 37.50% 512.50% 512.50%
5 50 12.00% 510.00% 510.00% 918.00% 48.00% 510.00% 48.00% 48.00% 510.00% 816.00%
6 60 35.00% 58.33% 610.00% 915.00% 610.00% 610.00% 46.67% 58.33% 610.00% 1016.67%
7 70 45.71% 68.57% 710.00% 1014.29% 710.00% 710.00% 57.14% 68.57% 710.00% 1115.71%
8 80 67.50% 67.50% 911.25% 1012.50% 810.00% 78.75% 78.75% 67.50% 911.25% 1215.00%
9 90 77.78% 66.67% 1112.22% 1112.22% 910.00% 77.78% 88.89% 66.67% 1213.33% 1314.44%
10 100 88.00% 88.00% 1212.00% 1212.00% 1010.00% 88.00% 99.00% 88.00% 1212.00% 1313.00%
11 200 199.50% 2010.00% 2412.00% 2010.00% 2211.00% 2010.00% 157.50% 126.00% 2512.50% 2311.50%
12 300 268.67% 3010.00% 3511.67% 3110.33% 3712.33% 279.00% 3110.33% 196.33% 3411.33% 3010.00%
13 400 399.75% 4310.75% 4411.00% 4010.00% 4611.50% 399.75% 4210.50% 246.00% 4411.00% 399.75%
14 500 459.00% 5911.80% 5310.60% 5110.20% 5310.60% 5010.00% 489.60% 367.20% 5310.60% 5210.40%
15 600 549.00% 6711.17% 6310.50% 6410.67% 6410.67% 559.17% 6210.33% 508.33% 599.83% 6210.33%
16 700 649.14% 7610.86% 7510.71% 7210.29% 7310.43% 669.43% 7010.00% 659.29% 689.71% 7110.14%
17 800 749.25% 9211.50% 8310.38% 8010.00% 8010.00% 739.13% 779.63% 759.38% 769.50% 9011.25%
18 900 869.56% 10311.44% 9310.33% 9410.44% 899.89% 849.33% 859.44% 839.22% 889.78% 9510.56%
19 1,000 939.30% 11611.60% 10310.30% 10310.30% 939.30% 979.70% 949.40% 959.50% 10110.10% 10510.50%
20 2,000 1829.10% 21210.60% 20710.35% 1899.45% 1959.75% 20510.25% 20010.00% 1979.85% 20210.10% 21110.55%
21 3,000 2598.63% 30810.27% 30310.10% 2668.87% 31810.60% 31510.50% 30210.07% 2879.57% 31010.33% 33211.07%
22 4,000 3629.05% 42910.73% 40810.20% 3699.23% 40510.13% 41710.43% 3979.93% 3779.43% 40510.13% 43110.78%
23 5,000 4669.32% 53110.62% 4969.92% 4609.20% 50810.16% 52510.50% 51310.26% 4889.76% 4929.84% 52110.42%
24 6,000 5569.27% 62610.43% 5949.90% 5739.55% 61310.22% 62210.37% 61910.32% 60610.10% 5829.70% 60910.15%
25 7,000 6579.39% 73310.47% 6929.89% 6879.81% 70210.03% 73010.43% 70810.11% 6939.90% 6809.71% 71810.26%
26 8,000 7549.43% 83310.41% 81110.14% 7829.78% 80910.11% 83410.43% 81610.20% 7859.81% 7649.55% 81210.15%
27 9,000 8559.50% 93610.40% 91110.12% 8859.83% 91010.11% 93210.36% 91410.16% 8839.81% 8549.49% 92010.22%
28 10,000 9689.68% 102610.26% 102110.21% 9759.75% 101210.12% 104610.46% 102110.21% 9709.70% 9479.47% 101410.14%
29 20,000 19549.77% 19979.99% 19869.93% 19879.94% 204310.22% 208210.41% 201710.09% 19539.77% 19619.81% 202010.10%
30 30,000 29989.99% 304810.16% 28979.66% 29799.93% 305710.19% 304910.16% 301210.04% 29749.91% 29729.91% 301410.05%
31 40,000 39899.97% 406010.15% 38929.73% 39729.93% 401410.04% 404010.10% 402610.07% 39779.94% 403210.08% 399810.00%
32 50,000 503310.07% 505410.11% 48679.73% 49489.90% 501110.02% 505210.10% 501810.04% 49779.95% 503010.06% 501010.02%
33 60,000 600910.02% 607110.12% 58949.82% 59769.96% 59839.97% 608610.14% 59809.97% 59959.99% 601510.03% 59919.99%
34 70,000 69929.99% 710610.15% 68929.85% 701810.03% 69489.93% 703310.05% 69669.95% 704710.07% 701310.02% 69859.98%
35 80,000 79729.97% 814110.18% 79209.90% 79769.97% 79579.95% 804410.06% 802510.03% 803110.04% 79539.94% 79819.98%
36 90,000 89909.99% 919310.21% 88879.87% 902010.02% 89579.95% 902610.03% 89929.99% 902810.03% 89539.95% 89549.95%
37 100,000 999910.00% 1013710.14% 99089.91% 1002610.03% 99719.97% 1002610.03% 1002810.03% 1002510.03% 99789.98% 99029.90%
38 200,000 2010410.05% 2006310.03% 198929.95% 2001110.01% 198749.94% 2019910.10% 198989.95% 2016310.08% 199559.98% 198419.92%
39 300,000 3000110.00% 3003410.01% 298799.96% 3013910.05% 298449.95% 3027210.09% 298909.96% 3022610.08% 299269.98% 297899.93%
40 400,000 4001310.00% 4006910.02% 398139.95% 4009810.02% 4009310.02% 4026110.07% 398599.96% 4027810.07% 398149.95% 397029.93%
41 500,000 499159.98% 4998410.00% 497529.95% 5000110.00% 5035710.07% 5023510.05% 498249.96% 5023010.05% 499119.98% 497919.96%
42 600,000 6001910.00% 598749.98% 596279.94% 6005110.01% 6047510.08% 6017710.03% 597619.96% 6014510.02% 6001510.00% 598569.98%
43 700,000 7003710.01% 698399.98% 697969.97% 6999410.00% 7060110.09% 7018010.03% 695779.94% 6997610.00% 7013810.02% 698629.98%
44 800,000 799499.99% 798519.98% 798729.98% 7996310.00% 8044710.06% 8029810.04% 796509.96% 798839.99% 8016710.02% 799209.99%
45 900,000 8999510.00% 897789.98% 899129.99% 9007010.01% 9033010.04% 9018010.02% 895749.95% 898659.99% 9021410.02% 9008210.01%
46 1,000,000 9995910.00% 997579.98% 10002610.00% 10023010.02% 10023010.02% 10035910.04% 995489.95% 998009.98% 9998510.00% 10010610.01%
47 2,000,000 1997929.99% 1995359.98% 20007710.00% 20014210.01% 20008310.00% 20052110.03% 1994039.97% 20031010.02% 1994479.97% 20069010.03%
48 3,000,000 2994519.98% 2996409.99% 29986710.00% 30031110.01% 30023410.01% 30034210.01% 2994619.98% 30065510.02% 2994409.98% 30059910.02%
49 4,000,000 3994189.99% 3994639.99% 39982210.00% 39991410.00% 40079210.02% 40003210.00% 3990329.98% 40065010.02% 40018310.00% 40069410.02%
50 5,000,000 4996209.99% 49989810.00% 4995089.99% 49993410.00% 50054410.01% 50002410.00% 4987589.98% 50088010.02% 49988010.00% 50095410.02%
51 6,000,000 5994769.99% 60034610.01% 5996829.99% 59997710.00% 60035710.01% 59976910.00% 5984389.97% 60077910.01% 60025510.00% 60092110.02%
52 7,000,000 6993239.99% 70045610.01% 69994810.00% 70033010.00% 70026610.00% 69983710.00% 6984289.98% 70041010.01% 70055110.01% 70045110.01%
53 8,000,000 7991119.99% 80011010.00% 79978810.00% 80023510.00% 80020110.00% 80015410.00% 7988859.99% 80056010.01% 80063810.01% 80031810.00%
54 9,000,000 8988249.99% 89991010.00% 89996110.00% 89982210.00% 90094910.01% 90063210.01% 8992439.99% 90044510.00% 90020910.00% 90000510.00%
55 10,000,000 9994409.99% 9993339.99% 100030610.00% 99996510.00% 100109310.01% 100046610.00% 9993379.99% 100020610.00% 99981410.00% 100004010.00%
56 20,000,000 200116210.01% 199983210.00% 200140910.01% 199934410.00% 200110510.01% 200012510.00% 199926910.00% 19984049.99% 199972010.00% 199963010.00%
57 30,000,000 299915710.00% 300055310.00% 300096910.00% 299922310.00% 300259310.01% 299999710.00% 299954810.00% 29981759.99% 299959210.00% 300019310.00%
58 40,000,000 399862010.00% 400068910.00% 400175410.00% 399904610.00% 400229710.01% 400067810.00% 399880410.00% 399868510.00% 399871110.00% 400071610.00%
59 50,000,000 499963210.00% 500222010.00% 500057310.00% 499863110.00% 500400810.01% 499979710.00% 499801710.00% 499889510.00% 499849410.00% 499973310.00%
60 60,000,000 600098910.00% 600295710.00% 600049610.00% 599806610.00% 600357310.01% 599845410.00% 599777610.00% 599849910.00% 599966610.00% 599952410.00%
61 70,000,000 699875210.00% 700422910.01% 700075510.00% 699958210.00% 700296210.00% 699686210.00% 699793310.00% 699851410.00% 700096510.00% 699944610.00%
62 80,000,000 799880710.00% 800278810.00% 800182710.00% 799765710.00% 800352510.00% 799650010.00% 799816510.00% 799938910.00% 800030810.00% 800103410.00%
63 90,000,000 899906110.00% 900229910.00% 900183210.00% 899911510.00% 900443710.00% 89948369.99% 899890210.00% 899896310.00% 900094710.00% 899960810.00%
64 100,000,000 999992210.00% 1000247510.00% 1000109110.00% 999844310.00% 1000386310.00% 99934789.99% 999941710.00% 999961010.00% 1000218010.00% 999952110.00%
65 200,000,000 1999743710.00% 2000377410.00% 2000218510.00% 2000141110.00% 1999984610.00% 1999303110.00% 1999916110.00% 2000028710.00% 2000230710.00% 2000056110.00%
66 300,000,000 2999835610.00% 3000058210.00% 3000633710.00% 2999986810.00% 2999981010.00% 2999309910.00% 2999891310.00% 2999907110.00% 3000368210.00% 3000028210.00%
67 400,000,000 3999604810.00% 3999737510.00% 4001179110.00% 3999503010.00% 4000101410.00% 3999212310.00% 4000189910.00% 4000031410.00% 4000573510.00% 3999867110.00%
68 500,000,000 4999527910.00% 5000043710.00% 5001143610.00% 4999241010.00% 5000512110.00% 4999067810.00% 4999882010.00% 5000031910.00% 5000663210.00% 4999886810.00%
69 600,000,000 5999172510.00% 5999759710.00% 6000859110.00% 5999255910.00% 6000799010.00% 5999021110.00% 6000389510.00% 5999877210.00% 6001095810.00% 5999770210.00%
70 700,000,000 6998989110.00% 6999775510.00% 7000649710.00% 6999402910.00% 7000958110.00% 6999453610.00% 7000379510.00% 6999701410.00% 7000516110.00% 7000174110.00%
71 800,000,000 7999189710.00% 7999700310.00% 8000331610.00% 7998965210.00% 8001607310.00% 7999612010.00% 8000414810.00% 7999510910.00% 8000293210.00% 8000375010.00%
72 900,000,000 8999120810.00% 8999838110.00% 9000096810.00% 8999008410.00% 9001313210.00% 8999608610.00% 9000641210.00% 8999565810.00% 9000197910.00% 9000609210.00%
73 1,000,000,000 9999394210.00% 9999733410.00% 10000241010.00% 9998691210.00% 10001195810.00% 9999888510.00% 10001038710.00% 9999606110.00% 10000183910.00% 10000027210.00%
74 2,000,000,000 19999431610.00% 19999528410.00% 19999257510.00% 19999947110.00% 20001436810.00% 19998985210.00% 20000478510.00% 19997929310.00% 20001784410.00% 20001221210.00%
75 3,000,000,000 29999914310.00% 29999593210.00% 29998912610.00% 29999229110.00% 30000225710.00% 29997901610.00% 30002544710.00% 29997551010.00% 30001654910.00% 30002472910.00%
76 4,000,000,000 40000123310.00% 40000228510.00% 39996540510.00% 39998447010.00% 40000693610.00% 39998905210.00% 40003303410.00% 39999612210.00% 40000474110.00% 40001672210.00%
77 5,000,000,000 49998900110.00% 50003412710.00% 49998494910.00% 49999032210.00% 49997828410.00% 49999535210.00% 50001981810.00% 50000170210.00% 49999052210.00% 50001592310.00%
78 6,000,000,000 59996300510.00% 60003326010.00% 59999916910.00% 60000024410.00% 59995743910.00% 60001717610.00% 60001658810.00% 60000904310.00% 59998703810.00% 60001703810.00%
79 7,000,000,000 69997157910.00% 70003228710.00% 70001446210.00% 69999086510.00% 69995649110.00% 70000709510.00% 70000146010.00% 70000794310.00% 69999152210.00% 70002629610.00%
80 8,000,000,000 79995983910.00% 80003117210.00% 80001683410.00% 79998588710.00% 79994299110.00% 79999530210.00% 80000338310.00% 80001274510.00% 80001122910.00% 80004061810.00%
81 9,000,000,000 89995781310.00% 90003037510.00% 90001614110.00% 89999275310.00% 89994181010.00% 89999775010.00% 90000218310.00% 90002338110.00% 89999171810.00% 90004607610.00%
82 10,000,000,000 99996799410.00% 100003779010.00% 100001727110.00% 99997648410.00% 99993768810.00% 100000792810.00% 99998573110.00% 100004133010.00% 99999177210.00% 100003601210.00%

Distribution des chiffres dans Pi

Après avoir compté les occurrences des chiffres de 0 à 9 dans les premiers 100 milliards de chiffres de pi, nous pouvons facilement découvrir que les chiffres de pi sont distribués de manière aléatoire et uniforme. Les fréquences des chiffres de 0 à 9 sont égales.

Source des données de pi

Nous proposons le téléchargement des premiers 100 milliards de chiffres de pi. Vous pouvez télécharger les données de pi depuis la page de téléchargement et les analyser ou les compiler vous-même.

Cliquez pour accéder à la page de téléchargement de pi.