Prime p₀= 2817435415769895047 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 58 2 106 2 22 2 34 2 52 2 (?)
a_n: 0 2 12 14 72 74 180 182 204 206 240 242 294 296
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: 296
Found by: Roadranner
db: batch=82, k=14, 10 58 106 22 34 52

STPT(10)	2817433691516922977	0 2 42 44 72 74 102 104 144 146	-1724252972070
TPT(14)	2817433863476615429	0 2 12 14 48 50 90 92 138 140 168 170 228 230	-1552293279618
SPT(16)	2817434340238555897	0 6 34 52 90 94 166 172 264 270 342 346 384 402 430 436	-1075531339150
SPT(16)	2817434443414883143	0 70 90 108 124 148 196 210 244 258 306 330 346 364 384 454	-972355011904
SPT(16)	2817434522783912501	0 12 26 60 68 108 150 152 156 158 200 240 248 282 296 308	-892985982546
SPT(16)	2817435327846565703	0 50 104 138 144 158 168 180 224 236 246 260 266 300 354 404	-87923329344
SPT(16)	2817435558404828833	0 10 28 36 64 96 118 138 316 336 358 390 418 426 444 454	142634933786
SPT(18)	2817435887345917801	0 18 28 40 66 78 106 172 192 376 396 462 490 502 528 540 550 568	471576022754
STPT(10)	2817436069779108857	0 2 72 74 102 104 132 134 204 206	654009213810
SPT(16)	2817436671542410657	0 4 22 36 70 90 120 132 244 256 286 306 340 354 372 376	1255772515610
STPT(10)	2817437319506105687	0 2 30 32 42 44 54 56 84 86	1903736210640