Prime p₀= 1543857397864293011 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 40 2 28 2 10 2 46 2 88 2 (?)
a_n: 0 2 36 38 78 80 108 110 120 122 168 170 258 260
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: 260
Found by: Theadalus
db: batch=78, k=14, 34 40 28 10 46 88

TPT(14)	1543856342109280049	0 2 30 32 90 92 132 134 210 212 222 224 270 272	-1055755012962
STPT(10)	1543856477305035977	0 2 30 32 72 74 114 116 144 146	-920559257034
SPT(16)	1543856490615976477	0 6 64 90 106 124 132 196 210 274 282 300 316 342 400 406	-907248316534
SPT(16)	1543857017647281193	0 84 106 114 120 178 268 288 316 336 426 484 490 498 520 604	-380217011818
SPT(16)	1543857048275906333	0 26 36 78 180 186 216 230 294 308 338 344 446 488 498 524	-349588386678
STPT(10)	1543857356299150757	0 2 42 44 72 74 102 104 144 146	-41565142254
SPT(18)	1543857493138153351	0 6 16 22 118 138 160 222 240 298 316 378 400 420 516 522 532 538	95273860340
SPT(16)	1543858201325578007	0 2 6 24 56 72 74 90 116 132 134 150 182 200 204 206	803461284996
STPT(10)	1543858497901871687	0 2 30 32 42 44 54 56 84 86	1100037578676
SPT(16)	1543858503652352521	0 36 58 60 138 166 186 238 258 310 330 358 436 438 460 496	1105788059510
STPT(10)	1543858559177423537	0 2 42 44 72 74 102 104 144 146	1161313130526