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	13,403,940,095,787,008
Reduced χ²	1.081
Degrees of freedom	88
p-value	0.282

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	−0.06σ
17	0	0	614,965,786,737,747,558,400	−0.16σ
18	2	0	3,792,289,018,216,251,392,000	+4.79σ
19	1	1	21,955,357,473,880,238,194,688	+0.15σ
20	8	5	119,656,698,232,661,149,220,864	+1.51σ
21	23	24	615,377,305,196,523,792,891,904	−0.25σ
22	120	118	2,992,971,438,910,558,267,506,688	+0.19σ
23	514	543	13,793,694,457,587,456,062,521,344	−1.26σ
24	2,328	2,377	60,347,413,251,949,784,339,578,880	−1.01σ
25	9,919	9,889	251,045,239,128,094,933,159,772,160	+0.30σ
26	39,063	39,175	994,525,370,392,013,980,410,314,752	−0.57σ
27	147,762	147,994	3,757,095,843,703,359,333,644,369,920	−0.60σ
28	533,190	533,837	13,552,381,436,214,641,229,618,479,104	−0.89σ
29	1,840,165	1,840,817	46,732,349,780,050,229,485,478,346,752	−0.48σ
30	6,069,933	6,074,697	154,216,754,274,179,217,963,230,429,184	−1.93σ
31	19,198,488	19,203,880	487,523,932,866,733,860,858,311,475,200	−1.23σ
32	58,222,520	58,211,760	1,477,806,921,502,283,862,327,408,197,632	+1.41σ
33	169,339,963	169,343,302	4,299,074,680,733,887,365,832,159,264,768	−0.26σ
34	473,192,631	473,165,107	12,012,120,431,463,097,046,989,820,395,520	+1.27σ
35	1,270,843,644	1,270,786,288	32,261,123,444,499,560,006,654,067,998,720	+1.61σ
36	3,282,895,254	3,282,864,578	83,341,235,564,953,750,679,541,466,005,504	+0.54σ
37	8,162,789,153	8,162,798,411	207,226,855,999,352,338,796,910,764,621,824	−0.10σ
38	19,547,918,513	19,547,754,090	496,253,786,735,300,725,948,944,725,573,632	+1.18σ
39	45,110,217,836	45,110,201,746	1,145,201,046,312,194,941,291,313,934,368,768	+0.08σ
40	100,370,110,264	100,370,198,885	2,548,072,328,044,652,691,917,525,777,121,280	−0.28σ
41	215,428,462,228	215,428,719,558	5,469,033,289,461,767,088,428,178,309,382,144	−0.55σ
42	446,246,190,957	446,245,204,798	11,328,711,813,885,134,591,637,908,797,521,920	+1.48σ
43	892,491,260,446	892,490,409,596	22,657,423,627,771,758,757,859,769,641,336,832	+0.90σ
44	1,724,129,729,506	1,724,129,200,356	43,770,022,917,284,480,220,586,166,053,765,120	+0.40σ
45	3,218,373,927,660	3,218,374,507,330	81,704,042,778,930,879,096,684,241,339,023,360	−0.32σ
46	5,807,070,882,601	5,807,067,045,835	147,422,511,970,669,707,130,713,134,757,576,704	+1.59σ
47	10,131,477,818,628	10,131,478,675,713	257,205,233,650,968,113,548,966,468,119,429,120	−0.27σ
48	17,096,870,180,853	17,096,870,265,264	434,033,831,785,977,726,448,110,184,255,455,232	−0.02σ
49	27,913,249,840,880	27,913,257,575,945	708,626,664,140,477,051,639,671,811,259,498,496	−1.46σ
50	44,102,943,384,112	44,102,946,969,989	1,119,630,129,341,862,900,968,425,360,577,265,664	−0.54σ
51	67,451,555,844,725	67,451,565,954,099	1,712,375,491,934,550,547,995,104,438,506,225,664	−1.23σ
52	99,880,215,086,483	99,880,203,432,034	2,535,632,939,980,099,066,453,731,900,563,390,464	+1.17σ
53	143,224,449,417,789	143,224,442,657,253	3,636,001,951,669,483,254,276,965,033,649,897,472	+0.56σ
54	198,922,826,834,724	198,922,837,023,970	5,050,002,710,652,246,444,889,688,575,859,228,672	−0.72σ
55	267,641,631,012,010	267,641,635,268,612	6,794,549,101,604,781,920,774,019,110,160,826,368	−0.26σ
56	348,889,997,932,485	348,889,988,832,291	8,857,180,078,877,483,266,010,742,996,550,549,504	+0.49σ
57	440,703,159,901,342	440,703,143,788,167	11,188,016,941,740,236,107,029,873,789,474,177,024	+0.77σ
58	539,481,488,525,734	539,481,434,637,211	13,695,675,911,439,908,809,061,915,256,242,044,928	+2.32σ
59	640,062,701,828,207	640,062,719,061,148	16,249,107,013,574,042,919,596,920,542,179,885,056	−0.68σ
60	736,072,107,072,554	736,072,126,920,268	18,686,473,065,608,832,289,524,386,279,456,768,000	−0.73σ
61	820,539,470,557,681	820,539,420,173,405	20,830,822,433,793,235,662,667,040,548,053,843,968	+1.76σ
62	886,711,929,630,156	886,711,954,058,355	22,510,727,468,776,510,734,730,053,200,795,140,096	−0.82σ
63	928,936,338,627,469	928,936,332,823,135	23,582,666,872,054,028,635,442,635,407,070,593,024	+0.19σ
64	943,450,933,613,074	943,450,963,023,494	23,951,146,041,929,827,601,454,957,849,485,508,608	−0.96σ
65	928,936,299,816,610	928,936,332,823,135	23,582,666,872,054,028,635,442,635,407,070,593,024	−1.08σ
66	886,711,971,011,084	886,711,954,058,380	22,510,727,468,777,148,254,205,240,602,898,989,056	+0.57σ
67	820,539,356,627,783	820,539,420,173,405	20,830,822,433,793,235,662,667,040,548,053,843,968	−2.22σ
68	736,072,125,682,322	736,072,126,920,268	18,686,473,065,608,832,289,524,386,279,456,768,000	−0.05σ
69	640,062,733,897,625	640,062,719,061,130	16,249,107,013,573,582,488,864,840,751,771,549,696	+0.59σ
70	539,481,469,893,097	539,481,434,637,226	13,695,675,911,440,296,043,113,510,567,149,568,000	+1.52σ
71	440,703,191,155,693	440,703,143,788,180	11,188,016,941,740,554,866,767,467,490,526,101,504	+2.26σ
72	348,889,960,932,602	348,889,988,832,291	8,857,180,078,877,483,266,010,742,996,550,549,504	−1.49σ
73	267,641,636,867,463	267,641,635,268,612	6,794,549,101,604,781,920,774,019,110,160,826,368	+0.10σ
74	198,922,842,917,279	198,922,837,023,970	5,050,002,710,652,246,444,889,688,575,859,228,672	+0.42σ
75	143,224,423,112,070	143,224,442,657,257	3,636,001,951,669,586,556,043,777,807,138,947,072	−1.63σ
76	99,880,206,621,122	99,880,203,432,032	2,535,632,939,980,027,050,364,868,138,473,881,600	+0.32σ
77	67,451,561,222,570	67,451,565,954,099	1,712,375,491,934,550,547,995,104,438,506,225,664	−0.58σ
78	44,102,945,054,925	44,102,946,969,991	1,119,630,129,341,894,629,368,232,141,006,045,184	−0.29σ
79	27,913,262,528,267	27,913,257,575,945	708,626,664,140,477,051,639,671,811,259,498,496	+0.94σ
80	17,096,862,622,552	17,096,870,265,264	434,033,831,785,990,048,873,151,422,235,934,720	−1.85σ
81	10,131,472,199,525	10,131,478,675,712	257,205,233,650,960,808,638,313,279,136,989,184	−2.03σ
82	5,807,069,726,622	5,807,067,045,835	147,422,511,970,669,707,130,713,134,757,576,704	+1.11σ
83	3,218,373,828,277	3,218,374,507,330	81,704,042,778,928,554,806,930,953,935,519,744	−0.38σ
84	1,724,129,962,636	1,724,129,200,356	43,770,022,917,284,323,423,261,539,522,576,384	+0.58σ
85	892,490,532,204	892,490,409,596	22,657,423,627,771,034,723,154,876,541,435,904	+0.13σ
86	446,245,882,509	446,245,204,798	11,328,711,813,884,811,773,616,618,880,368,640	+1.01σ
87	215,429,130,520	215,428,719,558	5,469,033,289,461,689,842,687,369,650,634,752	+0.89σ
88	100,370,551,332	100,370,198,885	2,548,072,328,044,697,944,086,581,595,865,088	+1.11σ
89	45,110,081,980	45,110,201,746	1,145,201,046,312,231,546,549,085,201,760,256	−0.56σ
90	19,547,875,187	19,547,754,090	496,253,786,735,314,849,237,376,159,449,088	+0.87σ
91	8,162,863,689	8,162,798,411	207,226,855,999,346,466,102,996,673,495,040	+0.72σ
92	3,282,884,375	3,282,864,578	83,341,235,564,953,462,449,165,314,293,760	+0.35σ
93	1,270,769,594	1,270,786,288	32,261,123,444,499,442,913,063,756,365,824	−0.47σ
94	473,177,098	473,165,107	12,012,120,431,462,925,910,203,980,316,672	+0.55σ
95	169,362,664	169,343,302	4,299,074,680,733,948,164,427,128,766,464	+1.49σ
96	58,211,233	58,211,760	1,477,806,921,502,310,039,500,242,288,640	−0.07σ
97	19,200,343	19,203,880	487,523,932,866,733,860,858,311,475,200	−0.81σ
98	6,077,046	6,074,697	154,216,754,274,174,837,508,905,369,600	+0.95σ
99	1,840,351	1,840,817	46,732,349,780,049,402,652,734,259,200	−0.34σ
100	533,045	533,837	13,552,381,436,214,592,851,106,856,960	−1.08σ
101	147,675	147,994	3,757,095,843,703,252,681,016,475,648	−0.83σ
102	39,503	39,175	994,525,370,392,042,292,834,729,984	+1.66σ
103	9,814	9,889	251,045,239,128,095,826,512,969,728	−0.75σ
104	2,398	2,377	60,347,413,251,948,710,597,754,880	+0.43σ
105	576	543	13,793,694,457,587,750,267,781,120	+1.40σ
106	116	118	2,992,971,438,910,600,680,308,736	−0.17σ
107	25	24	615,377,305,196,515,068,739,584	+0.15σ
108	8	5	119,656,698,232,662,843,719,680	+1.51σ
109	0	1	21,955,357,473,880,707,956,736	−0.93σ
110	1	0	3,792,289,018,216,197,390,336	+2.20σ
111	0	0	614,965,786,737,738,907,648	−0.16σ
112	0	0	93,343,021,201,259,986,944	−0.06σ
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