Prime p₀= 1237937191860377597 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 28 2 70 2 4 2 88 2 40 2 (?)
a_n: 0 2 12 14 42 44 114 116 120 122 210 212 252 254
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: 254
Found by: Cruncher Pete
db: batch=77, k=14, 10 28 70 4 88 40

SPT(16)	1237935777330469999	0 12 48 70 112 148 150 192 220 262 264 300 342 364 400 412	-1414529907598
TPT(14)	1237936234229152121	0 2 96 98 138 140 186 188 198 200 210 212 240 242	-957631225476
STPT(10)	1237936718650006337	0 2 30 32 42 44 54 56 84 86	-473210371260
STPT(10)	1237936795551951107	0 2 30 32 42 44 54 56 84 86	-396308426490
SPT(16)	1237937002827808441	0 12 46 72 82 112 120 130 138 148 156 186 196 222 256 268	-189032569156
STPT(10)	1237937077095251747	0 2 30 32 42 44 54 56 84 86	-114765125850
SPT(16)	1237937446437365189	0 24 32 54 90 98 102 110 222 230 234 242 278 300 308 332	254576987592
STPT(10)	1237937658705951911	0 2 36 38 78 80 120 122 156 158	466845574314
STPT(10)	1237937688139126031	0 2 36 38 78 80 120 122 156 158	496278748434
STPT(10)	1237937909935331777	0 2 42 44 72 74 102 104 144 146	718074954180
TPT(14)	1237938472854377309	0 2 42 44 72 74 78 80 138 140 198 200 222 224	1280993999712