Prime p₀= 1245261348786932129 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 40 2 4 2 88 2 40 2 40 2 (?)
a_n: 0 2 30 32 72 74 78 80 168 170 210 212 252 254
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: 254
Found by: Megacruncher
db: batch=77, k=14, 28 40 4 88 40 40

SPT(16)	1245259374038861173	0 18 24 46 66 76 88 100 144 156 168 178 198 220 226 244	-1974748070956
SPT(16)	1245260211741863167	0 42 64 144 154 174 180 222 274 316 322 342 352 432 454 496	-1137045068962
STPT(10)	1245260695394639387	0 2 90 92 102 104 114 116 204 206	-653392292742
SPT(16)	1245260750605914013	0 10 28 66 76 184 196 226 228 258 270 378 388 426 444 454	-598181018116
TPT(14)	1245261164707684181	0 2 30 32 66 68 78 80 168 170 180 182 336 338	-184079247948
STPT(10)	1245261297673767461	0 2 6 8 48 50 90 92 96 98	-51113164668
SPT(16)	1245261433550923807	0 22 40 82 222 244 256 286 300 330 342 364 504 546 564 586	84763991678
STPT(10)	1245261491064813317	0 2 30 32 42 44 54 56 84 86	142277881188
STPT(10)	1245261580767426977	0 2 60 62 72 74 84 86 144 146	231980494848
STPT(10)	1245261642031252127	0 2 60 62 72 74 84 86 144 146	293244319998
SPT(16)	1245262216362020821	0 6 12 96 100 150 160 240 262 342 352 402 406 490 496 502	867575088692