Prime p₀= 2960967122969130551 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 208 2 88 2 34 2 40 2 40 2 34 2 (?)
a_n: 0 2 210 212 300 302 336 338 378 380 420 422 456 458
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: 458
Found by: Landjunge
db: batch=82, k=14, 208 88 34 40 40 34

SPT(16)	2960965781864121851	0 2 8 18 36 56 68 102 176 210 222 242 260 270 276 278	-1341105008700
SPT(16)	2960965886362192889	0 20 24 38 78 102 108 120 122 134 140 164 204 218 222 242	-1236606937662
SPT(16)	2960965955455821251	0 2 30 50 72 92 110 120 158 168 186 206 228 248 276 278	-1167513309300
SPT(16)	2960966450380603529	0 20 30 68 78 98 128 134 138 144 174 194 204 242 252 272	-672588527022
SPT(16)	2960966796331805123	0 56 66 126 128 140 168 170 366 368 396 408 410 470 480 536	-326637325428
SPT(16)	2960966821705994993	0 8 36 48 50 56 114 126 128 140 198 204 206 218 246 254	-301263135558
STPT(10)	2960967122969130851	0 2 36 38 78 80 120 122 156 158	300
STPT(10)	2960967187679343497	0 2 54 56 72 74 90 92 144 146	64710212946
SPT(16)	2960967699260361547	0 4 22 30 40 42 60 84 100 124 142 144 154 162 180 184	576291230996
SPT(16)	2960967817215548411	0 6 18 32 116 152 162 168 200 206 216 252 336 350 362 368	694246417860
STPT(10)	2960968497796416617	0 2 42 44 72 74 102 104 144 146	1374827286066