Suffix match length (bits)

Fit to analytical expectation

Expected distribution assumes MD5 acts like a random function. The trailing run of matching bits has the same truncated-geometric distribution as the leading run, by exchangeability of bit positions.

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	13,403,995,930,361,856
Reduced χ²	1.255
Degrees of freedom	51
p-value	0.105

Per-bucket detail

Bucket	Observed	Expected (now)	Expected (end)	Residual
0	6,701,997,983,882,408	6,701,997,965,180,928	170,141,183,460,469,231,731,687,303,715,884,105,728	+0.23σ
1	3,350,998,977,937,858	3,350,998,982,590,464	85,070,591,730,234,615,865,843,651,857,942,052,864	−0.08σ
2	1,675,499,427,310,463	1,675,499,491,295,232	42,535,295,865,117,307,932,921,825,928,971,026,432	−1.56σ
3	837,749,773,481,196	837,749,745,647,616	21,267,647,932,558,653,966,460,912,964,485,513,216	+0.96σ
4	418,874,854,134,576	418,874,872,823,808	10,633,823,966,279,326,983,230,456,482,242,756,608	−0.91σ
5	209,437,477,821,091	209,437,436,411,904	5,316,911,983,139,663,491,615,228,241,121,378,304	+2.86σ
6	104,718,723,499,593	104,718,718,205,952	2,658,455,991,569,831,745,807,614,120,560,689,152	+0.52σ
7	52,359,366,794,751	52,359,359,102,976	1,329,227,995,784,915,872,903,807,060,280,344,576	+1.06σ
8	26,179,679,089,976	26,179,679,551,488	664,613,997,892,457,936,451,903,530,140,172,288	−0.09σ
9	13,089,830,499,761	13,089,839,775,744	332,306,998,946,228,968,225,951,765,070,086,144	−2.56σ
10	6,544,920,791,322	6,544,919,887,872	166,153,499,473,114,484,112,975,882,535,043,072	+0.35σ
11	3,272,457,285,947	3,272,459,943,936	83,076,749,736,557,242,056,487,941,267,521,536	−1.47σ
12	1,636,229,739,933	1,636,229,971,968	41,538,374,868,278,621,028,243,970,633,760,768	−0.18σ
13	818,114,250,839	818,114,985,984	20,769,187,434,139,310,514,121,985,316,880,384	−0.81σ
14	409,055,710,749	409,057,492,992	10,384,593,717,069,655,257,060,992,658,440,192	−2.79σ
15	204,529,798,527	204,528,746,496	5,192,296,858,534,827,628,530,496,329,220,096	+2.33σ
16	102,263,752,226	102,264,373,248	2,596,148,429,267,413,814,265,248,164,610,048	−1.94σ
17	51,132,363,773	51,132,186,624	1,298,074,214,633,706,907,132,624,082,305,024	+0.78σ
18	25,566,184,305	25,566,093,312	649,037,107,316,853,453,566,312,041,152,512	+0.57σ
19	12,783,047,690	12,783,046,656	324,518,553,658,426,726,783,156,020,576,256	+0.01σ
20	6,391,512,854	6,391,523,328	162,259,276,829,213,363,391,578,010,288,128	−0.13σ
21	3,195,702,743	3,195,761,664	81,129,638,414,606,681,695,789,005,144,064	−1.04σ
22	1,597,897,564	1,597,880,832	40,564,819,207,303,340,847,894,502,572,032	+0.42σ
23	798,941,295	798,940,416	20,282,409,603,651,670,423,947,251,286,016	+0.03σ
24	399,470,323	399,470,208	10,141,204,801,825,835,211,973,625,643,008	+0.01σ
25	199,733,769	199,735,104	5,070,602,400,912,917,605,986,812,821,504	−0.09σ
26	99,861,884	99,867,552	2,535,301,200,456,458,802,993,406,410,752	−0.57σ
27	49,938,121	49,933,776	1,267,650,600,228,229,401,496,703,205,376	+0.61σ
28	24,961,477	24,966,888	633,825,300,114,114,700,748,351,602,688	−1.08σ
29	12,481,725	12,483,444	316,912,650,057,057,350,374,175,801,344	−0.49σ
30	6,241,694	6,241,722	158,456,325,028,528,675,187,087,900,672	−0.01σ
31	3,119,398	3,120,861	79,228,162,514,264,337,593,543,950,336	−0.83σ
32	1,560,971	1,560,430	39,614,081,257,132,168,796,771,975,168	+0.43σ
33	779,910	780,215	19,807,040,628,566,084,398,385,987,584	−0.35σ
34	391,070	390,108	9,903,520,314,283,042,199,192,993,792	+1.54σ
35	195,072	195,054	4,951,760,157,141,521,099,596,496,896	+0.04σ
36	97,617	97,527	2,475,880,078,570,760,549,798,248,448	+0.29σ
37	48,810	48,763	1,237,940,039,285,380,274,899,124,224	+0.21σ
38	24,138	24,382	618,970,019,642,690,137,449,562,112	−1.56σ
39	12,185	12,191	309,485,009,821,345,068,724,781,056	−0.05σ
40	6,012	6,095	154,742,504,910,672,534,362,390,528	−1.07σ
41	3,123	3,048	77,371,252,455,336,267,181,195,264	+1.36σ
42	1,552	1,524	38,685,626,227,668,133,590,597,632	+0.72σ
43	809	762	19,342,813,113,834,066,795,298,816	+1.71σ
44	406	381	9,671,406,556,917,033,397,649,408	+1.28σ
45	173	190	4,835,703,278,458,516,698,824,704	−1.27σ
46	95	95	2,417,851,639,229,258,349,412,352	−0.02σ
47	44	48	1,208,925,819,614,629,174,706,176	−0.52σ
48	21	24	604,462,909,807,314,587,353,088	−0.58σ
49	6	12	302,231,454,903,657,293,676,544	−1.71σ
50	6	6	151,115,727,451,828,646,838,272	+0.02σ
51	3	3	75,557,863,725,914,323,419,136	+0.01σ
52	2	1	37,778,931,862,957,161,709,568	+0.42σ
53	0	1	18,889,465,931,478,580,854,784	−0.86σ
54	0	0	9,444,732,965,739,290,427,392	−0.61σ
55	0	0	4,722,366,482,869,645,213,696	−0.43σ
56	0	0	2,361,183,241,434,822,606,848	−0.30σ
57	0	0	1,180,591,620,717,411,303,424	−0.22σ
58	0	0	590,295,810,358,705,651,712	−0.15σ
59	0	0	295,147,905,179,352,825,856	−0.11σ
60	0	0	147,573,952,589,676,412,928	−0.08σ
61	0	0	73,786,976,294,838,206,464	−0.05σ
62	0	0	36,893,488,147,419,103,232	−0.04σ
63	0	0	18,446,744,073,709,551,616	−0.03σ
64	0	0	9,223,372,036,854,775,808	−0.02σ
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	−0.01σ
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