Prime p₀= 2749394654027505329 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 58 2 4 2 70 2 16 2 40 2 (?)
a_n: 0 2 42 44 102 104 108 110 180 182 198 200 240 242
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: 242
Found by: Roadranner
db: batch=82, k=14, 40 58 4 70 16 40

STPT(12)	2749393539151630727	0 2 30 32 72 74 180 182 222 224 252 254	-1114875874602
STPT(10)	2749393941945465497	0 2 12 14 72 74 132 134 144 146	-712082039832
SPT(16)	2749394180828044441	0 30 40 42 60 82 96 132 136 172 186 208 226 228 238 268	-473199460888
SPT(16)	2749394258955657847	0 30 46 76 132 156 160 202 270 312 316 340 396 426 442 472	-395071847482
STPT(10)	2749394423730174041	0 2 6 8 48 50 90 92 96 98	-230297331288
SPT(16)	2749394454605808679	0 24 54 70 88 102 138 204 238 304 340 354 372 388 418 442	-199421696650
STPT(10)	2749395066839536277	0 2 30 32 42 44 54 56 84 86	412812030948
SPT(16)	2749395071454750269	0 18 42 74 110 132 150 152 180 182 200 222 258 290 314 332	417427244940
SPT(18)	2749395280199381509	0 22 48 72 100 108 148 150 174 178 202 204 244 252 280 304 330 352	626171876180
STPT(12)	2749395621379395929	0 2 12 14 42 44 48 50 78 80 90 92	967351890600
STPT(10)	2749395698635387187	0 2 12 14 42 44 72 74 84 86	1044607881858