Prime p₀= 2637627497243684681 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 28 2 58 2 10 2 10 2 28 2 (?)
a_n: 0 2 36 38 66 68 126 128 138 140 150 152 180 182
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: 182
Found by: RFGuy_KCCO
db: batch=82, k=14, 34 28 58 10 10 28

SPT(16)	2637626179888075853	0 24 54 80 86 110 158 170 234 246 294 318 324 350 380 404	-1317355608828
STPT(10)	2637626238607684031	0 2 36 38 78 80 120 122 156 158	-1258636000650
SPT(16)	2637626274756658313	0 6 36 44 116 120 174 200 300 326 380 384 456 464 494 500	-1222487026368
STPT(10)	2637626649314514839	0 2 42 44 60 62 78 80 120 122	-847929169842
SPT(16)	2637627032825170453	0 6 18 36 70 96 126 138 148 160 190 216 250 268 280 286	-464418514228
SPT(16)	2637627144618032269	0 54 82 132 160 180 184 204 238 258 262 282 310 360 388 442	-352625652412
STPT(10)	2637627777244420967	0 2 30 32 42 44 54 56 84 86	280000736286
STPT(10)	2637628035460486097	0 2 120 122 162 164 204 206 324 326	538216801416
STPT(10)	2637628086524317487	0 2 30 32 42 44 54 56 84 86	589280632806
STPT(10)	2637628574353866617	0 2 30 32 42 44 54 56 84 86	1077110181936
STPT(10)	2637628666413301667	0 2 30 32 42 44 54 56 84 86	1169169616986