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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 | 6,074,853,283,069,952 |
| Reduced χ² | 0.751 |
| Degrees of freedom | 19 |
| p-value | 0.768 |
Per-bucket detail
| Bucket | Observed | Expected (now) | Expected (end) | Residual |
|---|---|---|---|---|
| 0 | 770,223,274,166,633 | 770,223,275,178,775 | 43,143,988,327,398,911,839,001,592,649,134,112,768 | −0.04σ |
| 1 | 1,643,142,974,391,768 | 1,643,142,987,048,046 | 92,040,508,431,783,893,168,652,104,264,117,649,408 | −0.31σ |
| 2 | 1,697,914,380,235,944 | 1,697,914,419,949,625 | 95,108,525,379,508,778,125,135,623,301,109,907,456 | −0.96σ |
| 3 | 1,131,942,988,291,561 | 1,131,942,946,633,089 | 63,405,683,586,339,506,537,677,917,336,614,469,632 | +1.24σ |
| 4 | 547,105,777,952,897 | 547,105,757,539,325 | 30,646,080,400,063,988,730,710,678,241,334,525,952 | +0.87σ |
| 5 | 204,252,803,204,147 | 204,252,816,148,016 | 11,441,203,349,357,332,742,463,916,492,546,113,536 | −0.91σ |
| 6 | 61,275,844,574,376 | 61,275,844,844,405 | 3,432,361,004,807,181,877,746,540,043,112,022,016 | −0.03σ |
| 7 | 15,173,071,366,746 | 15,173,066,342,424 | 849,917,963,095,110,807,779,068,966,638,452,736 | +1.29σ |
| 8 | 3,161,055,700,667 | 3,161,055,488,005 | 177,066,242,311,482,764,899,623,415,513,612,288 | +0.12σ |
| 9 | 561,964,235,095 | 561,965,420,090 | 31,478,443,077,596,722,717,297,399,482,548,224 | −1.58σ |
| 10 | 86,168,340,806 | 86,168,031,080 | 4,826,694,605,231,472,680,134,298,812,022,784 | +1.06σ |
| 11 | 11,489,202,743 | 11,489,070,811 | 643,559,280,697,530,613,021,776,860,413,952 | +1.23σ |
| 12 | 1,340,410,122 | 1,340,391,595 | 75,081,916,081,379,203,224,115,032,883,200 | +0.51σ |
| 13 | 137,490,336 | 137,476,061 | 7,700,709,341,679,872,637,146,343,931,904 | +1.22σ |
| 14 | 12,435,509 | 12,438,310 | 696,730,845,199,615,551,711,505,022,976 | −0.79σ |
| 15 | 995,477 | 995,065 | 55,738,467,615,969,043,937,843,216,384 | +0.41σ |
| 16 | 70,392 | 70,484 | 3,948,141,456,131,134,161,795,678,208 | −0.35σ |
| 17 | 4,475 | 4,423 | 247,726,522,737,639,952,775,905,280 | +0.79σ |
| 18 | 246 | 246 | 13,762,584,596,535,593,972,793,344 | +0.02σ |
| 19 | 12 | 12 | 676,056,787,198,236,050,849,792 | −0.02σ |
| 20 | 0 | 1 | 29,295,794,111,923,550,683,136 | −0.72σ |
| 21 | 0 | 0 | 1,116,030,251,882,795,630,592 | −0.14σ |
| 22 | 0 | 0 | 37,201,008,396,093,366,272 | −0.03σ |
| 23 | 0 | 0 | 1,078,290,098,437,485,696 | −0.00σ |
| 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 |