Prime p₀= 2356561043488287947 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 130 2 4 2 10 2 16 2 22 2 (?)
a_n: 0 2 42 44 174 176 180 182 192 194 210 212 234 236
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: 236
Found by: herby44
db: batch=81, k=14, 40 130 4 10 16 22

STPT(10)	2356558544990194211	0 2 6 8 18 20 30 32 36 38	-2498498093736
SPT(16)	2356559131859523167	0 24 44 56 66 110 114 134 156 176 180 224 234 246 266 290	-1911628764780
SPT(16)	2356559331657278893	0 28 40 54 60 126 178 210 214 246 298 364 370 384 396 424	-1711831009054
STPT(10)	2356560687795973847	0 2 24 26 42 44 60 62 84 86	-355692314100
TPT(14)	2356560719839045901	0 2 60 62 306 308 318 320 366 368 408 410 438 440	-323649242046
SPT(16)	2356560933959619067	0 16 30 64 72 120 132 156 160 184 196 244 252 286 300 316	-109528668880
STPT(10)	2356561093330280819	0 2 48 50 90 92 132 134 180 182	49841992872
SPT(16)	2356561584631479493	0 6 10 46 60 114 168 190 324 346 400 454 468 504 508 514	541143191546
SPT(16)	2356561602471287779	0 12 40 84 154 208 214 220 222 228 234 288 358 402 430 442	558982999832
TPT(14)	2356561747791079529	0 2 30 32 42 44 138 140 180 182 198 200 240 242	704302791582
SPT(16)	2356562019213416747	0 24 36 122 132 140 194 266 270 342 396 404 414 500 512 536	975725128800