Prime p₀= 2919336561158580257 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 52 2 16 2 10 2 148 2 16 2 (?)
a_n: 0 2 60 62 114 116 132 134 144 146 294 296 312 314
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: 314
Found by: Landjunge
db: batch=82, k=14, 58 52 16 10 148 16

SPT(16)	2919334705235170259	0 44 92 98 104 168 174 192 230 248 254 318 324 330 378 422	-1855923409998
SPT(18)	2919335142014880223	0 6 10 24 34 76 108 138 150 154 166 196 228 270 280 294 298 304	-1419143700034
STPT(12)	2919335530938292589	0 2 48 50 60 62 210 212 222 224 270 272	-1030220287668
SPT(16)	2919335584620944107	0 6 10 12 54 76 82 132 154 204 210 232 274 276 280 286	-976537636150
SPT(16)	2919335965312154677	0 22 42 60 112 136 154 220 246 312 330 354 406 424 444 466	-595846425580
SPT(16)	2919335997456730997	0 14 26 120 122 132 134 162 194 222 224 234 236 330 342 356	-563701849260
STPT(10)	2919336614829740429	0 2 42 44 60 62 78 80 120 122	53671160172
SPT(16)	2919337009197142951	0 6 30 46 60 88 198 216 250 268 378 406 420 436 460 466	448038562694
SPT(16)	2919337029057559939	0 64 78 82 90 132 184 208 234 258 310 352 360 364 378 442	467898979682
STPT(10)	2919337146040483031	0 2 78 80 108 110 138 140 216 218	584881902774
SPT(16)	2919337216018586777	0 36 56 60 74 84 122 260 276 414 452 462 476 480 500 536	654860006520