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Match count (nibble)
Fit to analytical expectation
Expected distribution assumes MD5 acts like a random function. The matching-nibble count is Binomial(32, 1/16): each of the 32 output nibbles matches its input nibble independently with probability 1/16.
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 | 2.000 | 2.000 |
| Std. deviation | 1.369 | 1.369 |
Pearson χ² test
| Samples | 13,404,004,520,296,448 |
| Reduced χ² | 0.689 |
| Degrees of freedom | 19 |
| p-value | 0.834 |
Per-bucket detail
| Bucket | Observed | Expected (now) | Expected (end) | Residual |
|---|---|---|---|---|
| 0 | 1,699,477,437,065,455 | 1,699,477,465,720,213 | 43,143,988,327,398,911,839,001,592,649,134,112,768 | −0.70σ |
| 1 | 3,625,551,959,286,048 | 3,625,551,926,869,770 | 92,040,508,431,783,893,168,652,104,264,117,649,408 | +0.54σ |
| 2 | 3,746,403,652,589,102 | 3,746,403,657,765,380 | 95,108,525,379,508,778,125,135,623,301,109,907,456 | −0.08σ |
| 3 | 2,497,602,443,658,808 | 2,497,602,438,510,266 | 63,405,683,586,339,506,537,677,917,336,614,469,632 | +0.10σ |
| 4 | 1,207,174,538,310,755 | 1,207,174,511,946,624 | 30,646,080,400,063,988,730,710,678,241,334,525,952 | +0.76σ |
| 5 | 450,678,459,981,597 | 450,678,484,460,078 | 11,441,203,349,357,332,742,463,916,492,546,113,536 | −1.15σ |
| 6 | 135,203,538,624,396 | 135,203,545,338,023 | 3,432,361,004,807,181,877,746,540,043,112,022,016 | −0.58σ |
| 7 | 33,478,975,304,620 | 33,478,973,131,320 | 849,917,963,095,110,807,779,068,966,638,452,736 | +0.38σ |
| 8 | 6,974,786,121,476 | 6,974,786,069,025 | 177,066,242,311,482,764,899,623,415,513,612,288 | +0.02σ |
| 9 | 1,239,960,351,012 | 1,239,961,967,827 | 31,478,443,077,596,722,717,297,399,482,548,224 | −1.45σ |
| 10 | 190,127,877,980 | 190,127,501,733 | 4,826,694,605,231,472,680,134,298,812,022,784 | +0.86σ |
| 11 | 25,350,404,361 | 25,350,333,564 | 643,559,280,697,530,613,021,776,860,413,952 | +0.44σ |
| 12 | 2,957,546,449 | 2,957,538,916 | 75,081,916,081,379,203,224,115,032,883,200 | +0.14σ |
| 13 | 303,370,633 | 303,337,325 | 7,700,709,341,679,872,637,146,343,931,904 | +1.91σ |
| 14 | 27,440,953 | 27,444,806 | 696,730,845,199,615,551,711,505,022,976 | −0.74σ |
| 15 | 2,197,077 | 2,195,584 | 55,738,467,615,969,043,937,843,216,384 | +1.01σ |
| 16 | 155,492 | 155,521 | 3,948,141,456,131,134,161,795,678,208 | −0.07σ |
| 17 | 9,652 | 9,758 | 247,726,522,737,639,952,775,905,280 | −1.07σ |
| 18 | 556 | 542 | 13,762,584,596,535,593,972,793,344 | +0.60σ |
| 19 | 26 | 27 | 676,056,787,198,236,050,849,792 | −0.12σ |
| 20 | 0 | 1 | 29,295,794,111,923,550,683,136 | −1.07σ |
| 21 | 0 | 0 | 1,116,030,251,882,795,630,592 | −0.21σ |
| 22 | 0 | 0 | 37,201,008,396,093,366,272 | −0.04σ |
| 23 | 0 | 0 | 1,078,290,098,437,485,696 | −0.01σ |
| 24 | 0 | 0 | 26,957,252,460,937,684 | −0.00σ |
| 25 | 0 | 0 | 575,088,052,499,991 | −0.00σ |
| 26 | 0 | 0 | 10,322,093,250,000 | −0.00σ |
| 27 | 0 | 0 | 152,919,900,000 | −0.00σ |
| 28 | 0 | 0 | 1,820,475,000 | −0.00σ |
| 29 | 0 | 0 | 16,740,000 | −0.00σ |
| 30 | 0 | 0 | 111,600 | −0.00σ |
| 31 | 0 | 0 | 480 | −0.00σ |
| 32 | 0 | 0 | 1 | −0.00σ |