Prime p₀= 2296568932580129087 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 10 2 28 2 124 2 22 2 46 2 (?)
a_n: 0 2 72 74 84 86 114 116 240 242 264 266 312 314
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: 314
Found by: Dirk Broer
db: batch=81, k=14, 70 10 28 124 22 46

STPT(10)	2296567350380290439	0 2 12 14 90 92 168 170 180 182	-1582199838648
SPT(16)	2296567515519208739	0 42 44 78 80 134 140 164 168 192 198 252 254 288 290 332	-1417060920348
SPT(16)	2296568009732901631	0 18 30 48 72 88 126 150 178 202 240 256 280 298 310 328	-922847227456
STPT(10)	2296568020185527117	0 2 12 14 42 44 72 74 84 86	-912394601970
SPT(16)	2296568337748250113	0 6 58 70 78 88 100 126 148 174 186 196 204 216 268 274	-594831878974
SPT(16)	2296568376901846651	0 16 18 42 58 112 130 132 196 198 216 270 286 310 312 328	-555678282436
SPT(16)	2296568976768718747	0 16 36 60 120 124 130 142 144 156 162 166 226 250 270 286	44188589660
SPT(16)	2296569023086894573	0 58 78 84 94 108 136 150 154 168 196 210 220 226 246 304	90506765486
STPT(10)	2296569410784050951	0 2 6 8 48 50 90 92 96 98	478203921864
STPT(10)	2296569574776076487	0 2 24 26 42 44 60 62 84 86	642195947400
SPT(16)	2296569912170787343	0 10 28 48 70 76 88 100 126 138 150 156 178 198 216 226	979590658256