Prime p₀= 2352713983664340341 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 70 2 28 2 40 2 28 2 76 2 (?)
a_n: 0 2 36 38 108 110 138 140 180 182 210 212 288 290
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: 290
Found by: Landjunge
db: batch=81, k=14, 34 70 28 40 28 76

SPT(16)	2352712897992797443	0 4 34 46 90 126 136 160 180 204 214 250 294 306 336 340	-1085671542898
SPT(16)	2352712960114256431	0 16 40 60 70 72 112 118 150 156 196 198 208 228 252 268	-1023550083910
TPT(14)	2352712970252068979	0 2 42 44 102 104 198 200 240 242 258 260 282 284	-1013412271362
SPT(16)	2352713305694340623	0 30 80 108 110 156 216 240 266 290 350 396 398 426 476 506	-677969999718
SPT(16)	2352713603483951251	0 36 42 52 70 102 108 118 120 130 136 168 186 196 202 238	-380180389090
SPT(16)	2352713648690657911	0 46 58 72 126 138 220 310 528 618 700 712 766 780 792 838	-334973682430
TPT(14)	2352714261256276259	0 2 18 20 60 62 108 110 180 182 198 200 222 224	277591935918
SPT(16)	2352714335622800129	0 18 30 38 44 110 144 168 224 248 282 348 354 362 374 392	351958459788
SPT(16)	2352714804228946753	0 4 10 46 66 70 84 88 186 190 204 208 228 264 270 274	820564606412
SPT(16)	2352715153792069657	0 24 42 52 64 114 120 132 142 154 160 210 222 232 250 274	1170127729316
STPT(10)	2352715169450074067	0 2 60 62 72 74 84 86 144 146	1185785733726