Prime p₀= 2497912325133783461 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 82 2 154 2 58 2 40 2 28 2 (?)
a_n: 0 2 36 38 120 122 276 278 336 338 378 380 408 410
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: 410
Found by: Penguin
db: batch=82, k=14, 34 82 154 58 40 28

SPT(16)	2497911398517286051	0 10 16 72 102 112 126 156 172 202 216 226 256 312 318 328	-926616497410
STPT(10)	2497911651896602301	0 2 6 8 48 50 90 92 96 98	-673237181160
SPT(16)	2497911738382969613	0 6 38 50 60 68 90 134 150 194 216 224 234 246 278 284	-586750813848
STPT(10)	2497911805572695957	0 2 30 32 42 44 54 56 84 86	-519561087504
SPT(16)	2497911928675271629	0 24 42 54 132 154 184 210 232 258 288 310 388 400 418 442	-396458511832
STPT(10)	2497912101421722257	0 2 24 26 42 44 60 62 84 86	-223712061204
STPT(10)	2497912335709742879	0 2 12 14 90 92 168 170 180 182	10575959418
SPT(16)	2497912473561675767	0 2 42 114 120 122 216 224 282 290 384 386 392 464 504 506	148427892306
SPT(16)	2497912507623033181	0 18 22 28 42 70 72 88 90 106 108 136 150 156 160 178	182489249720
SPT(16)	2497912811055696707	0 2 14 44 92 96 102 110 186 194 200 204 252 282 294 296	485921913246
SPT(16)	2497913040806484997	0 10 12 24 34 42 54 66 100 112 124 132 142 154 156 166	715672701536