Take a random base 10 number of 32 digits. The odds of a run of 4 or more identical digits is about 1 in 40.
At First occurrence prime gaps by Dr. Thomas R. Nicely, you can see the minimal primes generating a given gap up to 1998. Things get weird after the 1800's. The odds of a run of 4 or more in these prime numbers is about 1 in 4. Is this some artifact of the sieving method?
23333096984797, 111113196467011, 67777708053772723, 404444692323376357, 316129781931380000239027, 6787988999657777797, 33631026000015061369578943, 302233338032699490171225683, 3281312000028041064344397077, 612233338029222068547009577, 5739248000028792850873302491, 5972248000023708695939463647, 7500230000000254312587886349, 612233338029577635338157403, 7500230000004410741095419811, 7051230000020674054592576303, 512233338030056680994432863, 7500230000005824418875087691, 2644230000031218882264673171, 5851230000021967795781669357, 612233338029038274818850137, 8511230000017373935165665319, 5844230000028765302725127593, 7500230000005019060037933673, 65013315500001000157495421077531, 3039248000030181434897238311, 2844230000030892453360363713, 8012239000018115133439311463, 3044230000030128405583745033, 17361011751029174933335986203, 6139248000028643882072689133, 15251000000439240915164391943, 8051230000019922137852468729, 7500230000011523034496281371, 85982514713000000005643994785767