Prime p₀= 2098649694397534361 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 94 2 58 2 22 2 16 2 76 2 70 2 (?)
a_n: 0 2 96 98 156 158 180 182 198 200 276 278 348 350
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: 350
Found by: Landjunge
db: batch=80, k=14, 94 58 22 16 76 70

STPT(10)	2098648807635921659	0 2 18 20 30 32 42 44 60 62	-886761612702
SPT(16)	2098648937335152331	0 10 22 42 76 90 106 132 136 162 178 192 226 246 258 268	-757062382030
SPT(16)	2098649003666626909	0 40 60 78 82 120 138 144 208 214 232 270 274 292 312 352	-690730907452
STPT(10)	2098649026906852529	0 2 48 50 90 92 132 134 180 182	-667490681832
SPT(16)	2098649494768209151	0 6 10 28 40 60 82 88 90 96 118 138 150 168 172 178	-199629325210
TPT(14)	2098649627810636189	0 2 42 44 120 122 210 212 240 242 252 254 408 410	-66586898172
SPT(16)	2098649944295905577	0 20 24 42 132 224 234 252 254 272 282 374 464 482 486 506	249898371216
SPT(16)	2098650116619182843	0 14 36 66 78 90 134 150 194 210 254 266 278 308 330 344	422221648482
SPT(16)	2098651080147543661	0 12 18 28 42 130 132 148 150 166 168 256 270 280 286 298	1385750009300
SPT(16)	2098651677220499719	0 24 40 90 112 118 162 204 208 250 294 300 322 372 388 412	1982822965358
STPT(10)	2098651760359034651	0 2 108 110 138 140 168 170 276 278	2065961500290