Longest run (bit)

Fit to analytical expectation

Expected distribution assumes MD5 acts like a random function. The longest run of matching bits is the longest run of successes in 128 iid Bernoulli(1/2) trials.

Expected (now) scales that analytical distribution to the hashes computed so far; Expected (end) scales it to the full 2¹²⁸ keyspace. Residual is the Pearson residual (Observed − Expected) / √Expected in units of σ. A p-value near 1 means the observed distribution is consistent with random; near 0 means it is statistically surprising.

Distribution moments

	Observed	Expected
Mean	6.345	6.345
Std. deviation	1.808	1.808

Pearson χ² test

Samples	11,625,600,296,943,616
Reduced χ²	1.032
Degrees of freedom	55
p-value	0.410

Per-bucket detail

Bucket	Observed	Expected (now)	Expected (end)	Residual
0	0	0	1	−0.00σ
1	22,395	22,516	659,034,621,587,630,097,925,406,720	−0.80σ
2	291,499,898,776	291,499,349,599	8,532,212,195,821,815,690,880,246,022,668,288	+1.02σ
3	112,618,536,766,468	112,618,552,648,757	3,296,355,170,975,913,953,830,188,959,930,515,456	−1.50σ
4	1,251,977,056,377,580	1,251,977,028,978,022	36,645,480,308,082,511,851,021,400,638,691,999,744	+0.77σ
5	2,824,508,852,513,025	2,824,508,872,320,200	82,673,628,880,479,479,322,644,823,708,767,617,024	−0.37σ
6	2,899,000,223,445,533	2,899,000,184,093,584	84,853,996,279,826,276,904,832,134,827,802,099,712	+0.73σ
7	2,036,538,473,771,386	2,036,538,484,785,262	59,609,664,725,055,170,786,254,489,008,279,126,016	−0.24σ
8	1,193,961,597,326,998	1,193,961,605,048,834	34,947,363,628,659,461,790,319,163,908,382,785,536	−0.22σ
9	641,913,417,468,090	641,913,442,870,688	18,788,864,240,914,281,050,778,085,576,612,511,744	−1.00σ
10	331,013,434,290,491	331,013,422,872,318	9,688,792,676,555,938,900,437,062,740,284,014,592	+0.63σ
11	167,279,637,196,469	167,279,656,996,048	4,896,290,614,369,654,663,018,381,655,765,155,840	−1.53σ
12	83,709,426,232,349	83,709,415,892,876	2,450,182,136,494,551,671,684,016,167,970,668,544	+1.13σ
13	41,688,785,208,473	41,688,775,667,405	1,220,234,215,507,152,699,048,154,686,111,612,928	+1.48σ
14	20,712,601,879,694	20,712,600,250,035	606,259,673,319,599,880,347,246,183,495,761,920	+0.36σ
15	10,278,595,227,787	10,278,593,152,952	300,855,346,594,304,512,455,464,943,550,988,288	+0.65σ
16	5,097,593,234,826	5,097,592,751,191	149,206,998,577,991,209,378,836,738,748,710,912	+0.21σ
17	2,527,256,236,283	2,527,257,903,895	73,973,066,283,987,529,515,848,308,673,740,800	−1.05σ
18	1,252,692,438,267	1,252,694,546,403	36,666,482,107,675,219,043,251,232,052,346,880	−1.88σ
19	620,841,117,349	620,840,374,078	18,172,053,620,919,563,046,238,173,637,115,904	+0.94σ
20	307,656,908,425	307,657,205,640	9,005,154,096,268,711,410,902,028,827,754,496	−0.54σ
21	152,444,773,743	152,444,825,373	4,462,073,757,714,001,476,619,026,393,202,688	−0.13σ
22	75,530,101,949	75,529,975,847	2,210,769,190,266,126,692,521,262,933,082,112	+0.46σ
23	37,418,792,483	37,418,638,246	1,095,246,908,901,450,733,669,429,452,734,464	+0.80σ
24	18,536,106,264	18,536,112,882	542,553,692,176,791,364,042,806,156,853,248	−0.05σ
25	9,181,547,149	9,181,445,815	268,741,745,267,296,222,332,071,006,175,232	+1.06σ
26	4,547,285,920	4,547,415,802	133,103,269,771,812,244,771,443,784,548,352	−1.93σ
27	2,252,067,745	2,252,053,921	65,917,820,945,443,483,349,596,023,816,192	+0.29σ
28	1,115,180,993	1,115,199,869	32,642,000,522,382,460,409,973,449,949,184	−0.57σ
29	552,165,895	552,186,364	16,162,544,576,928,790,163,375,739,895,808	−0.87σ
30	273,388,592	273,386,391	8,002,044,277,822,173,577,045,157,609,472	+0.13σ
31	135,336,335	135,339,799	3,961,408,093,597,435,447,348,868,153,344	−0.30σ
32	66,990,928	66,993,201	1,960,897,014,663,724,363,714,689,761,280	−0.28σ
33	33,165,890	33,158,251	970,544,989,021,356,714,664,851,931,136	+1.33σ
34	16,408,803	16,409,951	480,320,734,825,442,019,587,219,521,536	−0.28σ
35	8,123,217	8,120,388	237,684,487,445,082,915,265,201,569,792	+0.99σ
36	4,015,703	4,017,900	117,604,303,709,282,379,604,275,757,056	−1.10σ
37	1,986,849	1,987,803	58,183,181,841,091,869,960,520,597,504	−0.68σ
38	981,388	983,328	28,782,105,912,148,008,868,761,305,088	−1.96σ
39	486,118	486,377	14,236,310,451,495,050,160,071,770,112	−0.37σ
40	240,244	240,545	7,040,783,973,369,295,364,287,365,120	−0.61σ
41	119,683	118,951	3,481,706,360,474,853,209,574,211,584	+2.12σ
42	59,245	58,815	1,721,510,367,127,723,403,177,361,408	+1.77σ
43	29,335	29,077	851,083,777,007,896,295,504,871,424	+1.51σ
44	14,481	14,373	420,706,185,225,708,090,270,154,752	+0.90σ
45	7,087	7,104	207,935,240,973,674,745,845,252,096	−0.20σ
46	3,451	3,511	102,758,694,667,234,116,821,319,680	−1.01σ
47	1,729	1,735	50,774,884,423,812,329,393,618,944	−0.14σ
48	891	857	25,085,210,757,003,087,223,717,888	+1.16σ
49	422	423	12,391,489,651,049,845,961,523,200	−0.07σ
50	226	209	6,120,186,961,799,037,648,371,712	+1.17σ
51	85	103	3,022,314,549,036,568,104,927,232	−1.80σ
52	62	51	1,492,267,808,586,806,813,786,112	+1.54σ
53	25	25	736,689,171,327,664,384,901,120	−0.03σ
54	12	12	363,622,219,180,962,614,345,728	−0.12σ
55	3	6	179,449,926,349,046,518,120,448	−1.26σ
56	3	3	88,544,371,553,805,847,756,800	−0.01σ
57	0	1	43,681,889,966,544,218,226,688	−1.22σ
58	4	1	21,545,797,078,092,756,287,488	+3.80σ
59	0	0	10,625,324,586,456,701,730,816	−0.60σ
60	0	0	5,238,875,316,933,512,658,944	−0.42σ
61	0	0	2,582,544,170,319,337,226,240	−0.30σ
62	0	0	1,272,825,341,085,959,061,504	−0.21σ
63	0	0	627,189,298,506,124,754,944	−0.15σ
64	0	0	308,982,963,234,634,989,568	−0.10σ
65	0	0	152,185,638,608,103,800,832	−0.07σ
66	0	0	74,939,897,799,445,053,440	−0.05σ
67	0	0	36,893,488,147,419,103,232	−0.04σ
68	0	0	18,158,513,697,557,839,872	−0.02σ
69	0	0	8,935,141,660,703,064,064	−0.02σ
70	0	0	4,395,513,236,313,604,096	−0.01σ
71	0	0	2,161,727,821,137,838,080	−0.01σ
72	0	0	1,062,849,512,059,437,056	−0.01σ
73	0	0	522,417,556,774,977,536	−0.00σ
74	0	0	256,705,178,760,118,272	−0.00σ
75	0	0	126,100,789,566,373,888	−0.00σ
76	0	0	61,924,494,876,344,320	−0.00σ
77	0	0	30,399,297,484,750,848	−0.00σ
78	0	0	14,918,173,765,664,768	−0.00σ
79	0	0	7,318,349,394,477,056	−0.00σ
80	0	0	3,588,805,953,060,864	−0.00σ
81	0	0	1,759,218,604,441,600	−0.00σ
82	0	0	862,017,116,176,384	−0.00σ
83	0	0	422,212,465,065,984	−0.00σ
84	0	0	206,708,186,021,888	−0.00σ
85	0	0	101,155,069,755,392	−0.00σ
86	0	0	49,478,023,249,920	−0.00σ
87	0	0	24,189,255,811,072	−0.00σ
88	0	0	11,819,749,998,592	−0.00σ
89	0	0	5,772,436,045,824	−0.00σ
90	0	0	2,817,498,546,176	−0.00σ
91	0	0	1,374,389,534,720	−0.00σ
92	0	0	670,014,898,176	−0.00σ
93	0	0	326,417,514,496	−0.00σ
94	0	0	158,913,789,952	−0.00σ
95	0	0	77,309,411,328	−0.00σ
96	0	0	37,580,963,840	−0.00σ
97	0	0	18,253,611,008	−0.00σ
98	0	0	8,858,370,048	−0.00σ
99	0	0	4,294,967,296	−0.00σ
100	0	0	2,080,374,784	−0.00σ
101	0	0	1,006,632,960	−0.00σ
102	0	0	486,539,264	−0.00σ
103	0	0	234,881,024	−0.00σ
104	0	0	113,246,208	−0.00σ
105	0	0	54,525,952	−0.00σ
106	0	0	26,214,400	−0.00σ
107	0	0	12,582,912	−0.00σ
108	0	0	6,029,312	−0.00σ
109	0	0	2,883,584	−0.00σ
110	0	0	1,376,256	−0.00σ
111	0	0	655,360	−0.00σ
112	0	0	311,296	−0.00σ
113	0	0	147,456	−0.00σ
114	0	0	69,632	−0.00σ
115	0	0	32,768	−0.00σ
116	0	0	15,360	−0.00σ
117	0	0	7,168	−0.00σ
118	0	0	3,328	−0.00σ
119	0	0	1,536	−0.00σ
120	0	0	704	−0.00σ
121	0	0	320	−0.00σ
122	0	0	144	−0.00σ
123	0	0	64	−0.00σ
124	0	0	28	−0.00σ
125	0	0	12	−0.00σ
126	0	0	5	−0.00σ
127	0	0	2	−0.00σ
128	0	0	1	−0.00σ