Prime p₀= 2956341197591196131 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 28 2 40 2 10 2 76 2 316 2 (?)
a_n: 0 2 6 8 36 38 78 80 90 92 168 170 486 488
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: 488
Found by: Ben
db: batch=82, k=14, 4 28 40 10 76 316

TPT(14)	2956340395032831239	0 2 12 14 30 32 42 44 138 140 198 200 240 242	-802558364892
TPT(14)	2956340526983834321	0 2 6 8 156 158 168 170 270 272 300 302 336 338	-670607361810
STPT(10)	2956340572288950941	0 2 6 8 48 50 90 92 96 98	-625302245190
STPT(10)	2956340661584570171	0 2 6 8 18 20 30 32 36 38	-536006625960
SPT(16)	2956341015531144161	0 12 50 68 78 98 140 152 228 240 282 302 312 330 368 380	-182060051970
SPT(16)	2956341131583969691	0 28 30 48 66 100 112 118 150 156 168 202 220 238 240 268	-66007226440
SPT(16)	2956341553839226037	0 44 90 134 176 200 216 240 260 284 300 324 366 410 456 500	356248029906
SPT(16)	2956341755702464471	0 40 66 82 88 102 130 168 220 258 286 300 306 322 348 388	558111268340
SPT(16)	2956341857891563223	0 8 54 68 78 140 176 216 278 318 354 416 426 440 486 494	660300367092
STPT(10)	2956342255089736991	0 2 30 32 78 80 126 128 156 158	1057498540860
SPT(16)	2956342300214468467	0 4 30 64 96 186 196 214 222 240 250 340 372 406 432 436	1102623272336