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	6,074,685,779,345,408
Reduced χ²	1.052
Degrees of freedom	54
p-value	0.370

Per-bucket detail

Bucket	Observed	Expected (now)	Expected (end)	Residual
0	0	0	1	−0.00σ
1	11,825	11,765	659,034,621,587,630,097,925,406,720	+0.55σ
2	152,316,853,774	152,316,173,657	8,532,212,195,821,815,690,880,246,022,668,288	+1.74σ
3	58,846,181,294,890	58,846,193,124,816	3,296,355,170,975,913,953,830,188,959,930,515,456	−1.54σ
4	654,191,335,365,460	654,191,341,499,962	36,645,480,308,082,511,851,021,400,638,691,999,744	−0.24σ
5	1,475,881,062,702,156	1,475,881,110,829,977	82,673,628,880,479,479,322,644,823,708,767,617,024	−1.25σ
6	1,514,804,852,871,304	1,514,804,805,155,983	84,853,996,279,826,276,904,832,134,827,802,099,712	+1.23σ
7	1,064,145,604,809,745	1,064,145,597,356,131	59,609,664,725,055,170,786,254,489,008,279,126,016	+0.23σ
8	623,876,738,916,621	623,876,737,374,274	34,947,363,628,659,461,790,319,163,908,382,785,536	+0.06σ
9	335,416,861,174,064	335,416,869,957,449	18,788,864,240,914,281,050,778,085,576,612,511,744	−0.48σ
10	172,963,328,625,511	172,963,329,319,309	9,688,792,676,555,938,900,437,062,740,284,014,592	−0.05σ
11	87,408,073,338,578	87,408,075,933,492	4,896,290,614,369,654,663,018,381,655,765,155,840	−0.28σ
12	43,740,411,054,474	43,740,399,233,874	2,450,182,136,494,551,671,684,016,167,970,668,544	+1.79σ
13	21,783,503,454,150	21,783,495,581,874	1,220,234,215,507,152,699,048,154,686,111,612,928	+1.69σ
14	10,822,884,004,986	10,822,885,268,577	606,259,673,319,599,880,347,246,183,495,761,920	−0.38σ
15	5,370,841,636,913	5,370,838,671,817	300,855,346,594,304,512,455,464,943,550,988,288	+1.28σ
16	2,663,630,671,118	2,663,627,976,501	149,206,998,577,991,209,378,836,738,748,710,912	+1.65σ
17	1,320,557,673,937	1,320,559,563,153	73,973,066,283,987,529,515,848,308,673,740,800	−1.64σ
18	654,564,727,016	654,566,263,464	36,666,482,107,675,219,043,251,232,052,346,880	−1.90σ
19	324,405,895,172	324,405,630,275	18,172,053,620,919,563,046,238,173,637,115,904	+0.47σ
20	160,758,865,532	160,759,083,770	9,005,154,096,268,711,410,902,028,827,754,496	−0.54σ
21	79,656,617,586	79,656,481,315	4,462,073,757,714,001,476,619,026,393,202,688	+0.48σ
22	39,466,452,330	39,466,423,967	2,210,769,190,266,126,692,521,262,933,082,112	+0.14σ
23	19,552,247,478	19,552,235,053	1,095,246,908,901,450,733,669,429,452,734,464	+0.09σ
24	9,685,611,347	9,685,612,652	542,553,692,176,791,364,042,806,156,853,248	−0.01σ
25	4,797,545,670	4,797,549,967	268,741,745,267,296,222,332,071,006,175,232	−0.06σ
26	2,376,064,615	2,376,145,868	133,103,269,771,812,244,771,443,784,548,352	−1.67σ
27	1,176,777,610	1,176,758,153	65,917,820,945,443,483,349,596,023,816,192	+0.57σ
28	582,704,803	582,721,633	32,642,000,522,382,460,409,973,449,949,184	−0.70σ
29	288,526,862	288,532,082	16,162,544,576,928,790,163,375,739,895,808	−0.31σ
30	142,838,361	142,851,671	8,002,044,277,822,173,577,045,157,609,472	−1.11σ
31	70,709,263	70,718,649	3,961,408,093,597,435,447,348,868,153,344	−1.12σ
32	35,000,837	35,005,732	1,960,897,014,663,724,363,714,689,761,280	−0.83σ
33	17,326,277	17,326,069	970,544,989,021,356,714,664,851,931,136	+0.05σ
34	8,575,079	8,574,636	480,320,734,825,442,019,587,219,521,536	+0.15σ
35	4,247,589	4,243,119	237,684,487,445,082,915,265,201,569,792	+2.17σ
36	2,099,018	2,099,460	117,604,303,709,282,379,604,275,757,056	−0.30σ
37	1,037,764	1,038,680	58,183,181,841,091,869,960,520,597,504	−0.90σ
38	513,063	513,815	28,782,105,912,148,008,868,761,305,088	−1.05σ
39	254,000	254,145	14,236,310,451,495,050,160,071,770,112	−0.29σ
40	125,268	125,691	7,040,783,973,369,295,364,287,365,120	−1.19σ
41	62,511	62,155	3,481,706,360,474,853,209,574,211,584	+1.43σ
42	30,804	30,732	1,721,510,367,127,723,403,177,361,408	+0.41σ
43	15,309	15,193	851,083,777,007,896,295,504,871,424	+0.94σ
44	7,521	7,510	420,706,185,225,708,090,270,154,752	+0.12σ
45	3,656	3,712	207,935,240,973,674,745,845,252,096	−0.92σ
46	1,763	1,834	102,758,694,667,234,116,821,319,680	−1.67σ
47	887	906	50,774,884,423,812,329,393,618,944	−0.65σ
48	468	448	25,085,210,757,003,087,223,717,888	+0.95σ
49	216	221	12,391,489,651,049,845,961,523,200	−0.35σ
50	121	109	6,120,186,961,799,037,648,371,712	+1.12σ
51	46	54	3,022,314,549,036,568,104,927,232	−1.08σ
52	36	27	1,492,267,808,586,806,813,786,112	+1.81σ
53	11	13	736,689,171,327,664,384,901,120	−0.59σ
54	8	6	363,622,219,180,962,614,345,728	+0.59σ
55	1	3	179,449,926,349,046,518,120,448	−1.23σ
56	2	2	88,544,371,553,805,847,756,800	+0.33σ
57	0	1	43,681,889,966,544,218,226,688	−0.88σ
58	2	0	21,545,797,078,092,756,287,488	+2.60σ
59	0	0	10,625,324,586,456,701,730,816	−0.44σ
60	0	0	5,238,875,316,933,512,658,944	−0.31σ
61	0	0	2,582,544,170,319,337,226,240	−0.21σ
62	0	0	1,272,825,341,085,959,061,504	−0.15σ
63	0	0	627,189,298,506,124,754,944	−0.11σ
64	0	0	308,982,963,234,634,989,568	−0.07σ
65	0	0	152,185,638,608,103,800,832	−0.05σ
66	0	0	74,939,897,799,445,053,440	−0.04σ
67	0	0	36,893,488,147,419,103,232	−0.03σ
68	0	0	18,158,513,697,557,839,872	−0.02σ
69	0	0	8,935,141,660,703,064,064	−0.01σ
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	−0.00σ
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