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Longest run (nibble)
Fit to analytical expectation
Expected distribution assumes MD5 acts like a random function. The longest run of matching nibbles is the longest run of successes in 32 iid Bernoulli(1/16) 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 | 0.989 | 0.989 |
| Std. deviation | 0.508 | 0.508 |
Pearson χ² test
| Samples | 6,074,775,973,658,624 |
| Reduced χ² | 1.130 |
| Degrees of freedom | 13 |
| p-value | 0.327 |
Per-bucket detail
| Bucket | Observed | Expected (now) | Expected (end) | Residual |
|---|---|---|---|---|
| 0 | 770,213,472,125,641 | 770,213,473,212,338 | 43,143,988,327,398,921,283,734,558,388,424,540,160 | −0.04σ |
| 1 | 4,645,801,323,980,294 | 4,645,801,312,029,282 | 260,237,459,546,942,687,931,752,451,700,818,968,576 | +0.18σ |
| 2 | 617,068,412,521,313 | 617,068,423,185,061 | 34,565,472,785,183,526,693,054,308,602,806,796,288 | −0.43σ |
| 3 | 39,167,239,090,029 | 39,167,236,121,713 | 2,193,977,172,333,603,584,333,072,206,416,314,368 | +0.47σ |
| 4 | 2,373,089,637,832 | 2,373,092,618,157 | 132,930,263,853,445,653,755,221,868,470,599,680 | −1.93σ |
| 5 | 143,248,506,602 | 143,248,592,658 | 8,024,159,307,146,040,819,035,019,268,849,664 | −0.23σ |
| 6 | 8,634,799,277 | 8,634,871,374 | 483,687,708,315,804,001,578,566,895,534,080 | −0.78σ |
| 7 | 519,758,467 | 519,789,782 | 29,116,349,011,495,305,633,480,149,303,296 | −1.37σ |
| 8 | 31,245,868 | 31,243,742 | 1,750,137,728,324,159,119,578,837,811,200 | +0.38σ |
| 9 | 1,873,658 | 1,875,039 | 105,031,475,201,429,518,770,711,298,048 | −1.01σ |
| 10 | 112,616 | 112,334 | 6,292,458,891,074,704,389,254,938,624 | +0.84σ |
| 11 | 6,569 | 6,717 | 376,278,161,354,999,660,715,966,464 | −1.81σ |
| 12 | 434 | 401 | 22,454,852,626,045,025,552,171,008 | +1.65σ |
| 13 | 22 | 24 | 1,337,020,010,462,468,032,692,224 | −0.38σ |
| 14 | 2 | 1 | 79,413,233,237,319,619,706,880 | +0.49σ |
| 15 | 0 | 0 | 4,703,919,738,795,935,662,080 | −0.29σ |
| 16 | 0 | 0 | 277,782,025,016,212,193,280 | −0.07σ |
| 17 | 0 | 0 | 16,348,066,647,354,900,480 | −0.02σ |
| 18 | 0 | 0 | 958,422,295,699,783,680 | −0.00σ |
| 19 | 0 | 0 | 55,943,151,621,242,880 | −0.00σ |
| 20 | 0 | 0 | 3,249,056,860,078,080 | −0.00σ |
| 21 | 0 | 0 | 187,604,171,489,280 | −0.00σ |
| 22 | 0 | 0 | 10,758,893,076,480 | −0.00σ |
| 23 | 0 | 0 | 612,032,839,680 | −0.00σ |
| 24 | 0 | 0 | 34,477,178,880 | −0.00σ |
| 25 | 0 | 0 | 1,918,894,080 | −0.00σ |
| 26 | 0 | 0 | 105,185,280 | −0.00σ |
| 27 | 0 | 0 | 5,652,480 | −0.00σ |
| 28 | 0 | 0 | 295,680 | −0.00σ |
| 29 | 0 | 0 | 14,880 | −0.00σ |
| 30 | 0 | 0 | 705 | −0.00σ |
| 31 | 0 | 0 | 30 | −0.00σ |
| 32 | 0 | 0 | 1 | −0.00σ |