Prime p₀= 2290572810683950601 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 64 2 82 2 4 2 10 2 106 2 (?)
a_n: 0 2 30 32 96 98 180 182 186 188 198 200 306 308
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: 308
Found by: Landjunge
db: batch=81, k=14, 28 64 82 4 10 106

SPT(16)	2290571345906662523	0 14 50 90 104 138 144 146 258 260 266 300 314 354 390 404	-1464777288078
SPT(16)	2290571545922296573	0 16 30 48 60 70 76 88 126 138 144 154 166 184 198 214	-1264761654028
SPT(16)	2290571611377483977	0 6 20 86 114 140 180 200 210 230 270 296 324 390 404 410	-1199306466624
TPT(14)	2290571713318236239	0 2 90 92 138 140 222 224 342 344 402 404 462 464	-1097365714362
SPT(16)	2290572190177278443	0 24 50 60 128 134 150 174 284 308 324 330 398 408 434 458	-620506672158
STPT(10)	2290572731587745219	0 2 18 20 30 32 42 44 60 62	-79096205382
SPT(16)	2290572830731791367	0 16 66 72 84 100 130 192 214 276 306 322 334 340 390 406	20047840766
SPT(16)	2290572924756157091	0 42 50 78 108 252 260 330 350 420 428 572 602 630 638 680	114072206490
SPT(16)	2290574432605751557	0 24 52 72 100 132 150 154 180 184 202 234 262 282 310 334	1621921800956
SPT(16)	2290574659514945057	0 74 102 114 116 132 146 192 224 270 284 300 302 314 342 416	1848830994456
SPT(16)	2290575048008127799	0 10 28 48 58 64 78 88 90 100 114 120 130 150 168 178	2237324177198