Prime p₀= 2310163088687714969 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 22 2 34 2 10 2 10 2 268 2 (?)
a_n: 0 2 18 20 42 44 78 80 90 92 102 104 372 374
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: 374
Found by: FritzB
db: batch=81, k=14, 16 22 34 10 10 268

SPT(16)	2310159464675637899	0 30 32 42 74 80 104 114 158 168 192 198 230 240 242 272	-3624012077070
SPT(16)	2310159645359301479	0 14 18 42 72 128 132 134 168 170 174 230 260 284 288 302	-3443328413490
TPT(14)	2310160736674130369	0 2 12 14 42 44 72 74 78 80 150 152 210 212	-2352013584600
SPT(16)	2310161865993726847	0 40 64 70 112 124 180 190 204 214 270 282 324 330 354 394	-1222693988122
STPT(10)	2310162113856129287	0 2 30 32 42 44 54 56 84 86	-974831585682
STPT(10)	2310162823888809287	0 2 30 32 72 74 114 116 144 146	-264798905682
SPT(16)	2310163224825504677	0 44 56 72 126 180 182 210 326 354 356 410 464 480 492 536	136137789708
SPT(16)	2310163274712999149	0 12 38 68 122 132 140 152 360 372 380 390 444 474 500 512	186025284180
TPT(14)	2310163365721187099	0 2 30 32 90 92 102 104 132 134 138 140 168 170	277033472130
STPT(12)	2310163679756294489	0 2 30 32 72 74 138 140 180 182 210 212	591068579520
SPT(16)	2310163762413141199	0 24 54 112 120 130 168 192 250 274 312 322 330 388 418 442	673725426230