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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 | 6,074,926,297,513,984 |
| Reduced χ² | 0.735 |
| Degrees of freedom | 6 |
| p-value | 0.622 |
Per-bucket detail
| Bucket | Observed | Expected (now) | Expected (end) | Residual |
|---|---|---|---|---|
| 0 | 5,706,166,713,760,024 | 5,706,166,703,950,157 | 319,626,579,315,078,477,702,860,203,058,987,532,288 | +0.13σ |
| 1 | 367,374,324,051,975 | 367,374,332,120,950 | 20,578,193,241,829,676,409,493,019,032,534,646,784 | −0.42σ |
| 2 | 1,380,208,813,197 | 1,380,210,518,097 | 77,311,440,327,981,424,594,731,781,555,486,720 | −1.45σ |
| 3 | 5,032,570,460 | 5,032,603,505 | 281,897,450,027,020,305,594,801,276,846,080 | −0.47σ |
| 4 | 18,252,166 | 18,255,212 | 1,022,551,769,974,266,797,027,644,932,096 | −0.71σ |
| 5 | 65,908 | 65,827 | 3,687,270,973,483,576,287,213,649,920 | +0.31σ |
| 6 | 252 | 236 | 13,203,902,706,800,148,453,785,600 | +1.06σ |
| 7 | 2 | 1 | 46,892,199,896,121,983,631,360 | +1.27σ |
| 8 | 0 | 0 | 164,869,745,483,616,092,160 | −0.05σ |
| 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 |