Match count (bit)

Fit to analytical expectation

Expected distribution assumes MD5 acts like a random function. The matching-bit count is Binomial(128, 1/2): each of the 128 input/output bit pairs matches independently with probability 1/2.

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	64.000	64.000
Std. deviation	5.657	5.657

Pearson χ² test

Samples	6,074,775,973,658,624
Reduced χ²	0.895
Degrees of freedom	86
p-value	0.746

Per-bucket detail

Bucket	Observed	Expected (now)	Expected (end)	Residual
0	0	0	1	−0.00σ
1	0	0	128	−0.00σ
2	0	0	8,128	−0.00σ
3	0	0	341,376	−0.00σ
4	0	0	10,668,000	−0.00σ
5	0	0	264,566,400	−0.00σ
6	0	0	5,423,611,200	−0.00σ
7	0	0	94,525,795,200	−0.00σ
8	0	0	1,429,702,652,400	−0.00σ
9	0	0	19,062,702,032,001	−0.00σ
10	0	0	226,846,154,180,785	−0.00σ
11	0	0	2,433,440,563,030,358	−0.00σ
12	0	0	23,726,045,489,546,000	−0.00σ
13	0	0	211,709,328,983,648,224	−0.00σ
14	0	0	1,739,040,916,651,418,880	−0.01σ
15	0	0	13,216,710,966,550,700,032	−0.02σ
16	0	0	93,343,021,201,261,314,048	−0.04σ
17	0	0	614,965,786,737,747,558,400	−0.10σ
18	2	0	3,792,289,018,216,251,392,000	+7.43σ
19	1	0	21,955,357,473,880,238,194,688	+0.97σ
20	3	2	119,656,698,232,661,149,220,864	+0.59σ
21	10	11	615,377,305,196,523,792,891,904	−0.30σ
22	58	53	2,992,971,438,910,558,267,506,688	+0.63σ
23	232	246	13,793,694,457,587,456,062,521,344	−0.91σ
24	1,058	1,077	60,347,413,251,949,784,339,578,880	−0.59σ
25	4,512	4,482	251,045,239,128,094,933,159,772,160	+0.45σ
26	17,567	17,754	994,525,370,392,013,980,410,314,752	−1.41σ
27	67,253	67,072	3,757,095,843,703,359,333,644,369,920	+0.70σ
28	241,551	241,939	13,552,381,436,214,641,229,618,479,104	−0.79σ
29	832,360	834,273	46,732,349,780,050,229,485,478,346,752	−2.09σ
30	2,750,276	2,753,102	154,216,754,274,179,217,963,230,429,184	−1.70σ
31	8,702,392	8,703,356	487,523,932,866,733,860,858,311,475,200	−0.33σ
32	26,386,978	26,382,049	1,477,806,921,502,283,862,327,408,197,632	+0.96σ
33	76,746,533	76,747,778	4,299,074,680,733,887,365,832,159,264,768	−0.14σ
34	214,445,062	214,442,321	12,012,120,431,463,097,046,989,820,395,520	+0.19σ
35	575,922,757	575,930,805	32,261,123,444,499,560,006,654,067,998,720	−0.34σ
36	1,487,860,727	1,487,821,247	83,341,235,564,953,750,679,541,466,005,504	+1.02σ
37	3,699,469,358	3,699,447,425	207,226,855,999,352,338,796,910,764,621,824	+0.36σ
38	8,859,151,367	8,859,203,043	496,253,786,735,300,725,948,944,725,573,632	−0.55σ
39	20,444,544,705	20,444,314,715	1,145,201,046,312,194,941,291,313,934,368,768	+1.61σ
40	45,488,657,953	45,488,600,240	2,548,072,328,044,652,691,917,525,777,121,280	+0.27σ
41	97,634,029,198	97,634,068,808	5,469,033,289,461,767,088,428,178,309,382,144	−0.13σ
42	202,242,653,888	202,241,999,673	11,328,711,813,885,134,591,637,908,797,521,920	+1.45σ
43	404,483,886,268	404,483,999,346	22,657,423,627,771,758,757,859,769,641,336,832	−0.18σ
44	781,389,401,566	781,389,544,190	43,770,022,917,284,480,220,586,166,053,765,120	−0.16σ
45	1,458,593,116,529	1,458,593,815,822	81,704,042,778,930,879,096,684,241,339,023,360	−0.58σ
46	2,631,812,806,916	2,631,810,580,723	147,422,511,970,669,707,130,713,134,757,576,704	+1.37σ
47	4,591,665,810,482	4,591,669,523,814	257,205,233,650,968,113,548,966,468,119,429,120	−1.73σ
48	7,748,445,027,831	7,748,442,321,436	434,033,831,785,977,726,448,110,184,255,455,232	+0.97σ
49	12,650,512,117,000	12,650,518,075,815	708,626,664,140,477,051,639,671,811,259,498,496	−1.68σ
50	19,987,816,067,185	19,987,818,559,786	1,119,630,129,341,862,900,968,425,360,577,265,664	−0.56σ
51	30,569,599,153,364	30,569,604,856,142	1,712,375,491,934,550,547,995,104,438,506,225,664	−1.03σ
52	45,266,537,315,350	45,266,530,267,751	2,535,632,939,980,099,066,453,731,900,563,390,464	+1.05σ
53	64,910,491,579,730	64,910,496,232,999	3,636,001,951,669,483,254,276,965,033,649,897,472	−0.58σ
54	90,153,462,137,019	90,153,466,990,280	5,050,002,710,652,246,444,889,688,575,859,228,672	−0.51σ
55	121,297,384,027,372	121,297,391,950,558	6,794,549,101,604,781,920,774,019,110,160,826,368	−0.72σ
56	158,119,831,626,474	158,119,814,506,974	8,857,180,078,877,483,266,010,742,996,550,549,504	+1.36σ
57	199,730,293,016,930	199,730,292,008,813	11,188,016,941,740,236,107,029,873,789,474,177,024	+0.07σ
58	244,497,437,089,676	244,497,426,424,569	13,695,675,911,439,908,809,061,915,256,242,044,928	+0.68σ
59	290,081,684,585,646	290,081,692,368,155	16,249,107,013,574,042,919,596,920,542,179,885,056	−0.46σ
60	333,593,919,255,263	333,593,946,223,355	18,686,473,065,608,832,289,524,386,279,456,768,000	−1.48σ
61	371,875,220,268,153	371,875,218,740,785	20,830,822,433,793,235,662,667,040,548,053,843,968	+0.08σ
62	401,865,146,130,794	401,865,155,736,009	22,510,727,468,776,510,734,730,053,200,795,140,096	−0.48σ
63	421,001,609,813,041	421,001,591,723,482	23,582,666,872,054,028,635,442,635,407,070,593,024	+0.88σ
64	427,579,713,168,248	427,579,741,594,160	23,951,146,041,929,827,601,454,957,849,485,508,608	−1.37σ
65	421,001,581,176,380	421,001,591,723,482	23,582,666,872,054,028,635,442,635,407,070,593,024	−0.51σ
66	401,865,172,980,014	401,865,155,736,021	22,510,727,468,777,148,254,205,240,602,898,989,056	+0.86σ
67	371,875,217,459,374	371,875,218,740,785	20,830,822,433,793,235,662,667,040,548,053,843,968	−0.07σ
68	333,593,946,240,256	333,593,946,223,355	18,686,473,065,608,832,289,524,386,279,456,768,000	+0.00σ
69	290,081,695,923,264	290,081,692,368,147	16,249,107,013,573,582,488,864,840,751,771,549,696	+0.21σ
70	244,497,443,393,705	244,497,426,424,576	13,695,675,911,440,296,043,113,510,567,149,568,000	+1.09σ
71	199,730,312,065,808	199,730,292,008,819	11,188,016,941,740,554,866,767,467,490,526,101,504	+1.42σ
72	158,119,815,700,706	158,119,814,506,974	8,857,180,078,877,483,266,010,742,996,550,549,504	+0.09σ
73	121,297,392,343,669	121,297,391,950,558	6,794,549,101,604,781,920,774,019,110,160,826,368	+0.04σ
74	90,153,473,578,923	90,153,466,990,280	5,050,002,710,652,246,444,889,688,575,859,228,672	+0.69σ
75	64,910,488,877,314	64,910,496,233,001	3,636,001,951,669,586,556,043,777,807,138,947,072	−0.91σ
76	45,266,532,205,027	45,266,530,267,749	2,535,632,939,980,027,050,364,868,138,473,881,600	+0.29σ
77	30,569,601,286,217	30,569,604,856,142	1,712,375,491,934,550,547,995,104,438,506,225,664	−0.65σ
78	19,987,817,563,366	19,987,818,559,787	1,119,630,129,341,894,629,368,232,141,006,045,184	−0.22σ
79	12,650,527,136,632	12,650,518,075,815	708,626,664,140,477,051,639,671,811,259,498,496	+2.55σ
80	7,748,440,994,836	7,748,442,321,436	434,033,831,785,990,048,873,151,422,235,934,720	−0.48σ
81	4,591,663,666,178	4,591,669,523,814	257,205,233,650,960,808,638,313,279,136,989,184	−2.73σ
82	2,631,811,991,398	2,631,810,580,723	147,422,511,970,669,707,130,713,134,757,576,704	+0.87σ
83	1,458,593,754,943	1,458,593,815,822	81,704,042,778,928,554,806,930,953,935,519,744	−0.05σ
84	781,389,016,708	781,389,544,190	43,770,022,917,284,323,423,261,539,522,576,384	−0.60σ
85	404,483,682,622	404,483,999,346	22,657,423,627,771,034,723,154,876,541,435,904	−0.50σ
86	202,242,749,670	202,241,999,673	11,328,711,813,884,811,773,616,618,880,368,640	+1.67σ
87	97,634,440,637	97,634,068,808	5,469,033,289,461,689,842,687,369,650,634,752	+1.19σ
88	45,488,534,900	45,488,600,240	2,548,072,328,044,697,944,086,581,595,865,088	−0.31σ
89	20,444,158,922	20,444,314,715	1,145,201,046,312,231,546,549,085,201,760,256	−1.09σ
90	8,859,336,374	8,859,203,043	496,253,786,735,314,849,237,376,159,449,088	+1.42σ
91	3,699,522,984	3,699,447,425	207,226,855,999,346,466,102,996,673,495,040	+1.24σ
92	1,487,830,019	1,487,821,247	83,341,235,564,953,462,449,165,314,293,760	+0.23σ
93	575,957,363	575,930,805	32,261,123,444,499,442,913,063,756,365,824	+1.11σ
94	214,449,032	214,442,321	12,012,120,431,462,925,910,203,980,316,672	+0.46σ
95	76,750,648	76,747,778	4,299,074,680,733,948,164,427,128,766,464	+0.33σ
96	26,381,622	26,382,049	1,477,806,921,502,310,039,500,242,288,640	−0.08σ
97	8,702,192	8,703,356	487,523,932,866,733,860,858,311,475,200	−0.39σ
98	2,753,667	2,753,102	154,216,754,274,174,837,508,905,369,600	+0.34σ
99	833,848	834,273	46,732,349,780,049,402,652,734,259,200	−0.47σ
100	241,808	241,939	13,552,381,436,214,592,851,106,856,960	−0.27σ
101	67,179	67,072	3,757,095,843,703,252,681,016,475,648	+0.41σ
102	17,946	17,754	994,525,370,392,042,292,834,729,984	+1.44σ
103	4,428	4,482	251,045,239,128,095,826,512,969,728	−0.80σ
104	1,082	1,077	60,347,413,251,948,710,597,754,880	+0.14σ
105	257	246	13,793,694,457,587,750,267,781,120	+0.69σ
106	52	53	2,992,971,438,910,600,680,308,736	−0.20σ
107	12	11	615,377,305,196,515,068,739,584	+0.31σ
108	3	2	119,656,698,232,662,843,719,680	+0.59σ
109	0	0	21,955,357,473,880,707,956,736	−0.63σ
110	1	0	3,792,289,018,216,197,390,336	+3.58σ
111	0	0	614,965,786,737,738,907,648	−0.10σ
112	0	0	93,343,021,201,259,986,944	−0.04σ
113	0	0	13,216,710,966,550,417,408	−0.02σ
114	0	0	1,739,040,916,651,406,848	−0.01σ
115	0	0	211,709,328,983,648,224	−0.00σ
116	0	0	23,726,045,489,545,660	−0.00σ
117	0	0	2,433,440,563,030,322	−0.00σ
118	0	0	226,846,154,180,790	−0.00σ
119	0	0	19,062,702,032,002	−0.00σ
120	0	0	1,429,702,652,400	−0.00σ
121	0	0	94,525,795,200	−0.00σ
122	0	0	5,423,611,200	−0.00σ
123	0	0	264,566,400	−0.00σ
124	0	0	10,668,000	−0.00σ
125	0	0	341,376	−0.00σ
126	0	0	8,128	−0.00σ
127	0	0	128	−0.00σ
128	0	0	1	−0.00σ