Prefix match length (bits)

Fit to analytical expectation

Expected distribution assumes MD5 acts like a random function. The leading run of matching bits has a truncated geometric distribution on 128 Bernoulli(1/2) trials — each additional matching bit halves the probability.

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	1.000	1.000
Std. deviation	1.414	1.414

Pearson χ² test

Samples	6,074,853,283,069,952
Reduced χ²	0.752
Degrees of freedom	50
p-value	0.902

Per-bucket detail

Bucket	Observed	Expected (now)	Expected (end)	Residual
0	3,037,426,598,783,528	3,037,426,641,534,976	170,141,183,460,469,231,731,687,303,715,884,105,728	−0.78σ
1	1,518,713,343,911,071	1,518,713,320,767,488	85,070,591,730,234,615,865,843,651,857,942,052,864	+0.59σ
2	759,356,687,581,135	759,356,660,383,744	42,535,295,865,117,307,932,921,825,928,971,026,432	+0.99σ
3	379,678,316,405,826	379,678,330,191,872	21,267,647,932,558,653,966,460,912,964,485,513,216	−0.71σ
4	189,839,178,833,327	189,839,165,095,936	10,633,823,966,279,326,983,230,456,482,242,756,608	+1.00σ
5	94,919,588,826,075	94,919,582,547,968	5,316,911,983,139,663,491,615,228,241,121,378,304	+0.64σ
6	47,459,787,531,242	47,459,791,273,984	2,658,455,991,569,831,745,807,614,120,560,689,152	−0.54σ
7	23,729,890,022,646	23,729,895,636,992	1,329,227,995,784,915,872,903,807,060,280,344,576	−1.15σ
8	11,864,943,868,621	11,864,947,818,496	664,613,997,892,457,936,451,903,530,140,172,288	−1.15σ
9	5,932,472,498,570	5,932,473,909,248	332,306,998,946,228,968,225,951,765,070,086,144	−0.58σ
10	2,966,235,477,741	2,966,236,954,624	166,153,499,473,114,484,112,975,882,535,043,072	−0.86σ
11	1,483,121,325,975	1,483,118,477,312	83,076,749,736,557,242,056,487,941,267,521,536	+2.34σ
12	741,559,207,849	741,559,238,656	41,538,374,868,278,621,028,243,970,633,760,768	−0.04σ
13	370,779,581,305	370,779,619,328	20,769,187,434,139,310,514,121,985,316,880,384	−0.06σ
14	185,389,470,025	185,389,809,664	10,384,593,717,069,655,257,060,992,658,440,192	−0.79σ
15	92,695,020,409	92,694,904,832	5,192,296,858,534,827,628,530,496,329,220,096	+0.38σ
16	46,347,341,978	46,347,452,416	2,596,148,429,267,413,814,265,248,164,610,048	−0.51σ
17	23,173,728,271	23,173,726,208	1,298,074,214,633,706,907,132,624,082,305,024	+0.01σ
18	11,586,844,512	11,586,863,104	649,037,107,316,853,453,566,312,041,152,512	−0.17σ
19	5,793,384,551	5,793,431,552	324,518,553,658,426,726,783,156,020,576,256	−0.62σ
20	2,896,673,996	2,896,715,776	162,259,276,829,213,363,391,578,010,288,128	−0.78σ
21	1,448,363,933	1,448,357,888	81,129,638,414,606,681,695,789,005,144,064	+0.16σ
22	724,199,620	724,178,944	40,564,819,207,303,340,847,894,502,572,032	+0.77σ
23	362,112,321	362,089,472	20,282,409,603,651,670,423,947,251,286,016	+1.20σ
24	181,040,997	181,044,736	10,141,204,801,825,835,211,973,625,643,008	−0.28σ
25	90,512,304	90,522,368	5,070,602,400,912,917,605,986,812,821,504	−1.06σ
26	45,263,737	45,261,184	2,535,301,200,456,458,802,993,406,410,752	+0.38σ
27	22,629,939	22,630,592	1,267,650,600,228,229,401,496,703,205,376	−0.14σ
28	11,314,653	11,315,296	633,825,300,114,114,700,748,351,602,688	−0.19σ
29	5,657,184	5,657,648	316,912,650,057,057,350,374,175,801,344	−0.20σ
30	2,827,765	2,828,824	158,456,325,028,528,675,187,087,900,672	−0.63σ
31	1,413,834	1,414,412	79,228,162,514,264,337,593,543,950,336	−0.49σ
32	708,176	707,206	39,614,081,257,132,168,796,771,975,168	+1.15σ
33	353,506	353,603	19,807,040,628,566,084,398,385,987,584	−0.16σ
34	177,077	176,802	9,903,520,314,283,042,199,192,993,792	+0.66σ
35	88,168	88,401	4,951,760,157,141,521,099,596,496,896	−0.78σ
36	43,946	44,200	2,475,880,078,570,760,549,798,248,448	−1.21σ
37	22,132	22,100	1,237,940,039,285,380,274,899,124,224	+0.21σ
38	10,927	11,050	618,970,019,642,690,137,449,562,112	−1.17σ
39	5,543	5,525	309,485,009,821,345,068,724,781,056	+0.24σ
40	2,756	2,763	154,742,504,910,672,534,362,390,528	−0.12σ
41	1,395	1,381	77,371,252,455,336,267,181,195,264	+0.37σ
42	671	691	38,685,626,227,668,133,590,597,632	−0.75σ
43	349	345	19,342,813,113,834,066,795,298,816	+0.20σ
44	164	173	9,671,406,556,917,033,397,649,408	−0.66σ
45	109	86	4,835,703,278,458,516,698,824,704	+2.44σ
46	45	43	2,417,851,639,229,258,349,412,352	+0.28σ
47	26	22	1,208,925,819,614,629,174,706,176	+0.95σ
48	16	11	604,462,909,807,314,587,353,088	+1.59σ
49	3	5	302,231,454,903,657,293,676,544	−1.03σ
50	2	3	151,115,727,451,828,646,838,272	−0.42σ
51	0	1	75,557,863,725,914,323,419,136	−1.16σ
52	1	1	37,778,931,862,957,161,709,568	+0.40σ
53	0	0	18,889,465,931,478,580,854,784	−0.58σ
54	0	0	9,444,732,965,739,290,427,392	−0.41σ
55	0	0	4,722,366,482,869,645,213,696	−0.29σ
56	0	0	2,361,183,241,434,822,606,848	−0.21σ
57	0	0	1,180,591,620,717,411,303,424	−0.15σ
58	0	0	590,295,810,358,705,651,712	−0.10σ
59	0	0	295,147,905,179,352,825,856	−0.07σ
60	0	0	147,573,952,589,676,412,928	−0.05σ
61	0	0	73,786,976,294,838,206,464	−0.04σ
62	0	0	36,893,488,147,419,103,232	−0.03σ
63	0	0	18,446,744,073,709,551,616	−0.02σ
64	0	0	9,223,372,036,854,775,808	−0.01σ
65	0	0	4,611,686,018,427,387,904	−0.01σ
66	0	0	2,305,843,009,213,693,952	−0.01σ
67	0	0	1,152,921,504,606,846,976	−0.00σ
68	0	0	576,460,752,303,423,488	−0.00σ
69	0	0	288,230,376,151,711,744	−0.00σ
70	0	0	144,115,188,075,855,872	−0.00σ
71	0	0	72,057,594,037,927,936	−0.00σ
72	0	0	36,028,797,018,963,968	−0.00σ
73	0	0	18,014,398,509,481,984	−0.00σ
74	0	0	9,007,199,254,740,992	−0.00σ
75	0	0	4,503,599,627,370,496	−0.00σ
76	0	0	2,251,799,813,685,248	−0.00σ
77	0	0	1,125,899,906,842,624	−0.00σ
78	0	0	562,949,953,421,312	−0.00σ
79	0	0	281,474,976,710,656	−0.00σ
80	0	0	140,737,488,355,328	−0.00σ
81	0	0	70,368,744,177,664	−0.00σ
82	0	0	35,184,372,088,832	−0.00σ
83	0	0	17,592,186,044,416	−0.00σ
84	0	0	8,796,093,022,208	−0.00σ
85	0	0	4,398,046,511,104	−0.00σ
86	0	0	2,199,023,255,552	−0.00σ
87	0	0	1,099,511,627,776	−0.00σ
88	0	0	549,755,813,888	−0.00σ
89	0	0	274,877,906,944	−0.00σ
90	0	0	137,438,953,472	−0.00σ
91	0	0	68,719,476,736	−0.00σ
92	0	0	34,359,738,368	−0.00σ
93	0	0	17,179,869,184	−0.00σ
94	0	0	8,589,934,592	−0.00σ
95	0	0	4,294,967,296	−0.00σ
96	0	0	2,147,483,648	−0.00σ
97	0	0	1,073,741,824	−0.00σ
98	0	0	536,870,912	−0.00σ
99	0	0	268,435,456	−0.00σ
100	0	0	134,217,728	−0.00σ
101	0	0	67,108,864	−0.00σ
102	0	0	33,554,432	−0.00σ
103	0	0	16,777,216	−0.00σ
104	0	0	8,388,608	−0.00σ
105	0	0	4,194,304	−0.00σ
106	0	0	2,097,152	−0.00σ
107	0	0	1,048,576	−0.00σ
108	0	0	524,288	−0.00σ
109	0	0	262,144	−0.00σ
110	0	0	131,072	−0.00σ
111	0	0	65,536	−0.00σ
112	0	0	32,768	−0.00σ
113	0	0	16,384	−0.00σ
114	0	0	8,192	−0.00σ
115	0	0	4,096	−0.00σ
116	0	0	2,048	−0.00σ
117	0	0	1,024	−0.00σ
118	0	0	512	−0.00σ
119	0	0	256	−0.00σ
120	0	0	128	−0.00σ
121	0	0	64	−0.00σ
122	0	0	32	−0.00σ
123	0	0	16	−0.00σ
124	0	0	8	−0.00σ
125	0	0	4	−0.00σ
126	0	0	2	−0.00σ
127	0	0	1	−0.00σ
128	0	0	1	−0.00σ