Prime p₀= 2514168346173448751 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 16 2 22 2 46 2 40 2 34 2 (?)
a_n: 0 2 48 50 66 68 90 92 138 140 180 182 216 218
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: [AF>Linux]Rogue 9
db: batch=82, k=14, 46 16 22 46 40 34

SPT(16)	2514166229224766833	0 48 94 136 156 208 238 276 418 456 486 538 558 600 646 694	-2116948681918
STPT(12)	2514166649663032751	0 2 90 92 210 212 288 290 408 410 498 500	-1696510416000
SPT(16)	2514166839129926809	0 34 52 82 100 118 148 190 252 294 324 342 360 390 408 442	-1507043521942
STPT(10)	2514167204845204859	0 2 18 20 30 32 42 44 60 62	-1141328243892
STPT(10)	2514167266078734179	0 2 42 44 90 92 138 140 180 182	-1080094714572
SPT(16)	2514167770718252213	0 24 50 60 78 108 120 134 174 188 200 230 248 258 284 308	-575455196538
STPT(10)	2514168358306449587	0 2 30 32 42 44 54 56 84 86	12133000836
STPT(10)	2514168659791371761	0 2 6 8 48 50 90 92 96 98	313617923010
SPT(16)	2514168837559563241	0 12 30 46 58 66 70 102 136 168 172 180 192 208 226 238	491386114490
STPT(10)	2514168990350339207	0 2 30 32 42 44 54 56 84 86	644176890456
SPT(16)	2514169043272267151	0 30 38 50 56 108 116 128 150 162 170 222 228 240 248 278	697098818400