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	11,625,578,822,107,136
Reduced χ²	0.939
Degrees of freedom	86
p-value	0.640

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	−0.14σ
18	2	0	3,792,289,018,216,251,392,000	+5.20σ
19	1	1	21,955,357,473,880,238,194,688	+0.29σ
20	8	4	119,656,698,232,661,149,220,864	+1.93σ
21	20	21	615,377,305,196,523,792,891,904	−0.22σ
22	102	102	2,992,971,438,910,558,267,506,688	−0.03σ
23	440	471	13,793,694,457,587,456,062,521,344	−1.44σ
24	2,001	2,062	60,347,413,251,949,784,339,578,880	−1.34σ
25	8,637	8,577	251,045,239,128,094,933,159,772,160	+0.65σ
26	33,813	33,977	994,525,370,392,013,980,410,314,752	−0.89σ
27	128,411	128,359	3,757,095,843,703,359,333,644,369,920	+0.14σ
28	462,206	463,010	13,552,381,436,214,641,229,618,479,104	−1.18σ
29	1,595,406	1,596,588	46,732,349,780,050,229,485,478,346,752	−0.94σ
30	5,264,021	5,268,739	154,216,754,274,179,217,963,230,429,184	−2.06σ
31	16,652,021	16,656,014	487,523,932,866,733,860,858,311,475,200	−0.98σ
32	50,498,681	50,488,543	1,477,806,921,502,283,862,327,408,197,632	+1.43σ
33	146,874,035	146,875,761	4,299,074,680,733,887,365,832,159,264,768	−0.14σ
34	410,410,930	410,388,155	12,012,120,431,463,097,046,989,820,395,520	+1.12σ
35	1,102,208,679	1,102,185,332	32,261,123,444,499,560,006,654,067,998,720	+0.70σ
36	2,847,368,262	2,847,312,107	83,341,235,564,953,750,679,541,466,005,504	+1.05σ
37	7,079,786,758	7,079,803,077	207,226,855,999,352,338,796,910,764,621,824	−0.19σ
38	16,954,307,468	16,954,265,264	496,253,786,735,300,725,948,944,725,573,632	+0.32σ
39	39,125,292,925	39,125,227,532	1,145,201,046,312,194,941,291,313,934,368,768	+0.33σ
40	87,053,593,482	87,053,631,260	2,548,072,328,044,652,691,917,525,777,121,280	−0.13σ
41	186,846,774,245	186,846,818,314	5,469,033,289,461,767,088,428,178,309,382,144	−0.10σ
42	387,040,660,201	387,039,837,935	11,328,711,813,885,134,591,637,908,797,521,920	+1.32σ
43	774,080,182,837	774,079,675,870	22,657,423,627,771,758,757,859,769,641,336,832	+0.58σ
44	1,495,381,327,103	1,495,381,192,022	43,770,022,917,284,480,220,586,166,053,765,120	+0.11σ
45	2,791,378,436,626	2,791,378,225,108	81,704,042,778,930,879,096,684,241,339,023,360	+0.13σ
46	5,036,620,758,357	5,036,617,232,260	147,422,511,970,669,707,130,713,134,757,576,704	+1.57σ
47	8,787,287,460,031	8,787,289,639,262	257,205,233,650,968,113,548,966,468,119,429,120	−0.74σ
48	14,828,551,546,885	14,828,551,266,253	434,033,831,785,977,726,448,110,184,255,455,232	+0.07σ
49	24,209,871,023,520	24,209,879,618,376	708,626,664,140,477,051,639,671,811,259,498,496	−1.75σ
50	38,251,608,886,580	38,251,609,797,031	1,119,630,129,341,862,900,968,425,360,577,265,664	−0.15σ
51	58,502,448,293,574	58,502,462,042,516	1,712,375,491,934,550,547,995,104,438,506,225,664	−1.80σ
52	86,628,658,142,922	86,628,645,716,805	2,535,632,939,980,099,066,453,731,900,563,390,464	+1.34σ
53	124,222,214,904,705	124,222,208,952,397	3,636,001,951,669,483,254,276,965,033,649,897,472	+0.53σ
54	172,530,836,358,575	172,530,845,767,224	5,050,002,710,652,246,444,889,688,575,859,228,672	−0.72σ
55	232,132,396,782,488	232,132,410,668,627	6,794,549,101,604,781,920,774,019,110,160,826,368	−0.91σ
56	302,601,206,711,713	302,601,178,193,025	8,857,180,078,877,483,266,010,742,996,550,549,504	+1.64σ
57	382,233,087,120,791	382,233,067,191,198	11,188,016,941,740,236,107,029,873,789,474,177,024	+1.02σ
58	467,906,043,032,176	467,905,996,044,373	13,695,675,911,439,908,809,061,915,256,242,044,928	+2.17σ
59	555,142,685,280,998	555,142,707,171,334	16,249,107,013,574,042,919,596,920,542,179,885,056	−0.93σ
60	638,414,091,059,179	638,414,113,246,989	18,686,473,065,608,832,289,524,386,279,456,768,000	−0.88σ
61	711,674,795,201,844	711,674,749,193,357	20,830,822,433,793,235,662,667,040,548,053,843,968	+1.72σ
62	769,067,854,672,891	769,067,874,128,304	22,510,727,468,776,510,734,730,053,200,795,140,096	−0.70σ
63	805,690,169,631,587	805,690,153,848,783	23,582,666,872,054,028,635,442,635,407,070,593,024	+0.56σ
64	818,279,035,383,517	818,279,062,502,668	23,951,146,041,929,827,601,454,957,849,485,508,608	−0.95σ
65	805,690,136,966,745	805,690,153,848,783	23,582,666,872,054,028,635,442,635,407,070,593,024	−0.59σ
66	769,067,873,466,329	769,067,874,128,326	22,510,727,468,777,148,254,205,240,602,898,989,056	−0.02σ
67	711,674,708,942,135	711,674,749,193,357	20,830,822,433,793,235,662,667,040,548,053,843,968	−1.51σ
68	638,414,096,470,367	638,414,113,246,989	18,686,473,065,608,832,289,524,386,279,456,768,000	−0.66σ
69	555,142,729,617,191	555,142,707,171,318	16,249,107,013,573,582,488,864,840,751,771,549,696	+0.95σ
70	467,906,010,166,116	467,905,996,044,387	13,695,675,911,440,296,043,113,510,567,149,568,000	+0.65σ
71	382,233,103,886,189	382,233,067,191,209	11,188,016,941,740,554,866,767,467,490,526,101,504	+1.88σ
72	302,601,158,756,064	302,601,178,193,025	8,857,180,078,877,483,266,010,742,996,550,549,504	−1.12σ
73	232,132,404,393,531	232,132,410,668,627	6,794,549,101,604,781,920,774,019,110,160,826,368	−0.41σ
74	172,530,846,248,661	172,530,845,767,224	5,050,002,710,652,246,444,889,688,575,859,228,672	+0.04σ
75	124,222,197,418,862	124,222,208,952,400	3,636,001,951,669,586,556,043,777,807,138,947,072	−1.03σ
76	86,628,650,235,644	86,628,645,716,803	2,535,632,939,980,027,050,364,868,138,473,881,600	+0.49σ
77	58,502,459,878,657	58,502,462,042,516	1,712,375,491,934,550,547,995,104,438,506,225,664	−0.28σ
78	38,251,609,811,285	38,251,609,797,032	1,119,630,129,341,894,629,368,232,141,006,045,184	+0.00σ
79	24,209,884,634,171	24,209,879,618,376	708,626,664,140,477,051,639,671,811,259,498,496	+1.02σ
80	14,828,543,635,095	14,828,551,266,253	434,033,831,785,990,048,873,151,422,235,934,720	−1.98σ
81	8,787,284,343,899	8,787,289,639,261	257,205,233,650,960,808,638,313,279,136,989,184	−1.79σ
82	5,036,617,940,257	5,036,617,232,260	147,422,511,970,669,707,130,713,134,757,576,704	+0.32σ
83	2,791,377,949,036	2,791,378,225,108	81,704,042,778,928,554,806,930,953,935,519,744	−0.17σ
84	1,495,381,138,462	1,495,381,192,022	43,770,022,917,284,323,423,261,539,522,576,384	−0.04σ
85	774,079,612,931	774,079,675,870	22,657,423,627,771,034,723,154,876,541,435,904	−0.07σ
86	387,040,625,441	387,039,837,935	11,328,711,813,884,811,773,616,618,880,368,640	+1.27σ
87	186,847,175,643	186,846,818,314	5,469,033,289,461,689,842,687,369,650,634,752	+0.83σ
88	87,053,875,840	87,053,631,260	2,548,072,328,044,697,944,086,581,595,865,088	+0.83σ
89	39,125,137,367	39,125,227,532	1,145,201,046,312,231,546,549,085,201,760,256	−0.46σ
90	16,954,398,982	16,954,265,264	496,253,786,735,314,849,237,376,159,449,088	+1.03σ
91	7,079,836,402	7,079,803,077	207,226,855,999,346,466,102,996,673,495,040	+0.40σ
92	2,847,313,349	2,847,312,107	83,341,235,564,953,462,449,165,314,293,760	+0.02σ
93	1,102,175,327	1,102,185,332	32,261,123,444,499,442,913,063,756,365,824	−0.30σ
94	410,397,984	410,388,155	12,012,120,431,462,925,910,203,980,316,672	+0.49σ
95	146,893,130	146,875,761	4,299,074,680,733,948,164,427,128,766,464	+1.43σ
96	50,486,485	50,488,543	1,477,806,921,502,310,039,500,242,288,640	−0.29σ
97	16,654,349	16,656,014	487,523,932,866,733,860,858,311,475,200	−0.41σ
98	5,271,225	5,268,739	154,216,754,274,174,837,508,905,369,600	+1.08σ
99	1,596,540	1,596,588	46,732,349,780,049,402,652,734,259,200	−0.04σ
100	462,356	463,010	13,552,381,436,214,592,851,106,856,960	−0.96σ
101	128,096	128,359	3,757,095,843,703,252,681,016,475,648	−0.73σ
102	34,149	33,977	994,525,370,392,042,292,834,729,984	+0.93σ
103	8,512	8,577	251,045,239,128,095,826,512,969,728	−0.70σ
104	2,057	2,062	60,347,413,251,948,710,597,754,880	−0.10σ
105	491	471	13,793,694,457,587,750,267,781,120	+0.91σ
106	98	102	2,992,971,438,910,600,680,308,736	−0.42σ
107	23	21	615,377,305,196,515,068,739,584	+0.43σ
108	8	4	119,656,698,232,662,843,719,680	+1.93σ
109	0	1	21,955,357,473,880,707,956,736	−0.87σ
110	1	0	3,792,289,018,216,197,390,336	+2.42σ
111	0	0	614,965,786,737,738,907,648	−0.14σ
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