Prime p₀= 1016809367349163457 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 166 2 46 2 10 2 136 2 28 2 (?)
a_n: 0 2 24 26 192 194 240 242 252 254 390 392 420 422
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: MarkRBright
db: batch=76, k=14, 22 166 46 10 136 28

TPT(14)	1016808027274747817	0 2 30 32 42 44 90 92 102 104 114 116 180 182	-1340074415640
SPT(16)	1016808664333296517	0 40 46 82 90 96 160 172 204 216 280 286 294 330 336 376	-703015866940
SPT(16)	1016808785065649729	0 14 30 74 102 158 164 192 200 228 234 290 318 362 378 392	-582283513728
STPT(12)	1016808973307209139	0 2 12 14 72 74 120 122 180 182 192 194	-394041954318
SPT(16)	1016808998138890927	0 22 36 46 54 66 102 106 150 154 190 202 210 220 234 256	-369210272530
STPT(10)	1016809257642667121	0 2 6 8 48 50 90 92 96 98	-109706496336
SPT(16)	1016809456347786379	0 4 28 40 42 48 84 130 132 178 214 220 222 234 258 262	88998622922
SPT(16)	1016809534626244267	0 34 42 46 52 96 154 192 244 282 340 384 390 394 402 436	167277080810
SPT(16)	1016810174797596727	0 66 70 94 136 190 204 216 304 316 330 384 426 450 454 520	807448433270
STPT(10)	1016810204180271869	0 2 18 20 30 32 42 44 60 62	836831108412
STPT(10)	1016810219834117711	0 2 36 38 78 80 120 122 156 158	852484954254