Prime p₀= 2275133169557894507 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 100 2 64 2 58 2 10 2 10 2 (?)
a_n: 0 2 12 14 114 116 180 182 240 242 252 254 264 266
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 266
Found by: Landjunge
db: batch=81, k=14, 10 100 64 58 10 10

SPT(16)	2275131732156050749	0 34 64 70 78 90 94 100 168 174 178 190 198 204 234 268	-1437401843758
STPT(10)	2275132025509558511	0 2 6 8 18 20 30 32 36 38	-1144048335996
SPT(16)	2275132264691732423	0 26 120 126 138 168 228 230 306 308 368 398 410 416 510 536	-904866162084
SPT(16)	2275132370652068429	0 8 12 54 78 90 102 104 138 140 152 164 188 230 234 242	-798905826078
STPT(10)	2275132371487566299	0 2 18 20 60 62 102 104 120 122	-798070328208
SPT(16)	2275132634069884607	0 20 36 42 102 104 132 174 272 314 342 344 404 410 426 446	-535488009900
STPT(10)	2275133701223350577	0 2 30 32 42 44 54 56 84 86	531665456070
STPT(10)	2275134279973663679	0 2 18 20 30 32 42 44 60 62	1110415769172
STPT(12)	2275134419140497587	0 2 30 32 114 116 180 182 264 266 294 296	1249582603080
STPT(10)	2275134931008570089	0 2 18 20 30 32 42 44 60 62	1761450675582
SPT(16)	2275135216274155717	0 6 72 94 100 130 136 184 252 300 306 336 342 364 430 436	2046716261210