Prime p₀= 3006514867851089807 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 22 2 4 2 28 2 22 2 28 2 (?)
a_n: 0 2 60 62 84 86 90 92 120 122 144 146 174 176
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: 176
Found by: MarkRBright
db: batch=82, k=14, 58 22 4 28 22 28

SPT(16)	3006512346919871057	0 20 32 72 74 114 116 144 272 300 302 342 344 384 396 416	-2520931218750
SPT(16)	3006512527767467437	0 6 24 60 112 136 186 214 252 280 330 354 406 442 460 466	-2340083622370
SPT(16)	3006512930563462163	0 74 86 90 114 116 126 140 174 188 198 200 224 228 240 314	-1937287627644
SPT(16)	3006513669705648001	0 12 28 30 78 120 130 132 238 240 250 292 340 342 358 370	-1198145441806
SPT(16)	3006513846284681179	0 12 28 58 84 160 172 220 342 390 402 478 504 534 550 562	-1021566408628
STPT(10)	3006514134136627529	0 2 18 20 30 32 42 44 60 62	-733714462278
STPT(10)	3006514874219401211	0 2 30 32 120 122 210 212 240 242	6368311404
STPT(10)	3006515317544928899	0 2 48 50 90 92 132 134 180 182	449693839092
SPT(16)	3006515638562704907	0 2 14 20 30 42 66 72 74 80 104 116 126 132 144 146	770711615100
SPT(16)	3006516020884176259	0 28 84 88 90 118 132 154 288 310 324 352 354 358 414 442	1153033086452
STPT(10)	3006516075201681797	0 2 30 32 42 44 54 56 84 86	1207350591990