Prime p₀= 2765579958708984581 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 142 2 106 2 46 2 70 2 40 2 (?)
a_n: 0 2 6 8 150 152 258 260 306 308 378 380 420 422
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: 422
Found by: Coleslaw
db: batch=82, k=14, 4 142 106 46 70 40

STPT(10)	2765577061777010021	0 2 30 32 78 80 126 128 156 158	-2896931974560
TPT(14)	2765577082678574999	0 2 30 32 42 44 102 104 198 200 228 230 240 242	-2876030409582
TPT(14)	2765577448201641707	0 2 72 74 132 134 210 212 240 242 324 326 384 386	-2510507342874
STPT(10)	2765579210798460569	0 2 42 44 60 62 78 80 120 122	-747910524012
TPT(14)	2765579537947443251	0 2 138 140 270 272 336 338 348 350 378 380 390 392	-420761541330
SPT(16)	2765579805516841367	0 6 36 54 116 146 174 176 234 236 264 294 356 374 404 410	-153192143214
STPT(12)	2765580118243168691	0 2 36 38 48 50 78 80 90 92 126 128	159534184110
SPT(16)	2765580629188307527	0 46 70 72 156 172 190 220 336 366 384 400 484 486 510 556	670479322946
SPT(16)	2765580842153776291	0 10 16 36 42 60 108 112 186 190 238 256 262 282 288 298	883444791710
SPT(16)	2765581014646678733	0 36 38 50 66 120 126 150 194 218 224 278 294 306 308 344	1055937694152
SPT(16)	2765581045610780753	0 30 44 54 68 180 198 230 234 266 284 396 410 420 434 464	1086901796172