Prime p₀= 2311141394942006909 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 22 2 124 2 28 2 58 2 10 2 (?)
a_n: 0 2 18 20 42 44 168 170 198 200 258 260 270 272
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: 272
Found by: Vato
db: batch=81, k=14, 16 22 124 28 58 10

SPT(18)	2311140613521219197	0 56 60 72 92 182 210 230 260 306 336 356 384 474 494 506 510 566	-781420787712
TPT(14)	2311140635795680079	0 2 108 110 138 140 210 212 222 224 240 242 252 254	-759146326830
SPT(18)	2311140665796183503	0 8 18 24 74 116 120 128 140 144 156 164 168 210 260 266 276 284	-729145823406
TPT(14)	2311140760522575659	0 2 12 14 60 62 138 140 192 194 198 200 318 320	-634419431250
SPT(16)	2311141122653606777	0 30 44 62 134 140 174 182 372 380 414 420 492 510 524 554	-272288400132
STPT(10)	2311141383583538291	0 2 30 32 60 62 90 92 120 122	-11358468618
SPT(16)	2311141413191937187	0 12 24 70 96 136 166 196 210 240 270 310 336 382 394 406	18249930278
SPT(16)	2311141524269820257	0 54 92 140 152 170 222 306 320 404 456 474 486 534 572 626	129327813348
STPT(10)	2311141624367994557	0 2 12 14 42 44 72 74 84 86	229425987648
STPT(10)	2311141854540356657	0 2 30 32 42 44 54 56 84 86	459598349748
SPT(16)	2311142066815123627	0 10 54 64 70 112 120 130 186 196 204 246 252 262 306 316	671873116718