Prime p₀= 2679666037348265681 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 28 2 46 2 70 2 10 2 4 2 (?)
a_n: 0 2 48 50 78 80 126 128 198 200 210 212 216 218
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: 218
Found by: JayPi
db: batch=82, k=14, 46 28 46 70 10 4

SPT(16)	2679664453259839301	0 20 26 72 120 156 182 230 252 300 326 362 410 456 462 482	-1584088426380
TPT(14)	2679665197357465409	0 2 30 32 42 44 78 80 198 200 252 254 318 320	-839990800272
SPT(16)	2679665495661047939	0 42 44 48 90 170 192 272 300 380 402 482 524 528 530 572	-541687217742
STPT(10)	2679665575254101261	0 2 36 38 78 80 120 122 156 158	-462094164420
SPT(16)	2679665590380451447	0 12 36 46 54 84 106 120 136 150 172 202 210 220 244 256	-446967814234
STPT(10)	2679665706481991369	0 2 18 20 30 32 42 44 60 62	-330866274312
STPT(10)	2679666166426324217	0 2 72 74 102 104 132 134 204 206	129078058536
STPT(10)	2679666263813568941	0 2 6 8 18 20 30 32 36 38	226465303260
SPT(16)	2679666304263061957	0 60 64 100 112 120 244 246 280 282 406 414 426 462 466 526	266914796276
SPT(16)	2679666658166118109	0 48 90 124 184 198 220 238 240 258 280 294 354 388 430 478	620817852428
SPT(16)	2679666769523919113	0 26 30 38 110 116 156 210 224 278 318 324 396 404 408 434	732175653432