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Longest run (byte)
Fit to analytical expectation
Expected distribution assumes MD5 acts like a random function. The longest run of matching bytes is the longest run of successes in 16 iid Bernoulli(1/256) trials.
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 | 0.061 | 0.061 |
| Std. deviation | 0.240 | 0.240 |
Pearson χ² test
| Samples | 11,625,488,627,793,920 |
| Reduced χ² | 2.217 |
| Degrees of freedom | 6 |
| p-value | 0.038 |
Per-bucket detail
| Bucket | Observed | Expected (now) | Expected (end) | Residual |
|---|---|---|---|---|
| 0 | 10,919,799,395,234,435 | 10,919,799,331,922,046 | 319,626,579,315,078,477,702,860,203,058,987,532,288 | +0.61σ |
| 1 | 703,038,280,886,865 | 703,038,343,356,240 | 20,578,193,241,829,676,409,493,019,032,534,646,784 | −2.36σ |
| 2 | 2,641,285,771,273 | 2,641,286,642,220 | 77,311,440,327,981,424,594,731,781,555,486,720 | −0.54σ |
| 3 | 9,630,843,450 | 9,630,812,284 | 281,897,450,027,020,305,594,801,276,846,080 | +0.32σ |
| 4 | 34,930,660 | 34,934,705 | 1,022,551,769,974,266,797,027,644,932,096 | −0.68σ |
| 5 | 126,757 | 125,973 | 3,687,270,973,483,576,287,213,649,920 | +2.21σ |
| 6 | 476 | 451 | 13,203,902,706,800,148,453,785,600 | +1.17σ |
| 7 | 4 | 2 | 46,892,199,896,121,983,631,360 | +1.89σ |
| 8 | 0 | 0 | 164,869,745,483,616,092,160 | −0.08σ |
| 9 | 0 | 0 | 572,526,699,699,240,960 | −0.00σ |
| 10 | 0 | 0 | 1,957,152,172,277,760 | −0.00σ |
| 11 | 0 | 0 | 6,554,187,202,560 | −0.00σ |
| 12 | 0 | 0 | 21,340,815,360 | −0.00σ |
| 13 | 0 | 0 | 66,716,160 | −0.00σ |
| 14 | 0 | 0 | 195,585 | −0.00σ |
| 15 | 0 | 0 | 510 | −0.00σ |
| 16 | 0 | 0 | 1 | −0.00σ |