Prime p₀= 2491585891858090427 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 82 2 88 2 4 2 22 2 4 2 (?)
a_n: 0 2 30 32 114 116 204 206 210 212 234 236 240 242
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: Ben
db: batch=82, k=14, 28 82 88 4 22 4

STPT(12)	2491584717737980607	0 2 12 14 42 44 120 122 150 152 162 164	-1174120109820
SPT(16)	2491584861169441363	0 30 84 88 144 184 186 210 214 238 240 280 336 340 394 424	-1030688649064
SPT(16)	2491585044319924087	0 6 10 16 34 54 100 124 126 150 196 216 234 240 244 250	-847538166340
STPT(10)	2491585445594719289	0 2 12 14 30 32 48 50 60 62	-446263371138
STPT(10)	2491585710274177211	0 2 30 32 60 62 90 92 120 122	-181583913216
SPT(16)	2491585875383522341	0 28 30 76 78 166 198 208 240 250 282 370 372 418 420 448	-16474568086
SPT(16)	2491586308940285783	0 14 30 36 80 140 146 156 224 234 240 300 344 350 366 380	417082195356
STPT(10)	2491587022688725571	0 2 30 32 78 80 126 128 156 158	1130830635144
STPT(10)	2491587057031329557	0 2 24 26 42 44 60 62 84 86	1165173239130
SPT(16)	2491587257803142269	0 24 28 58 60 94 112 130 162 180 198 232 234 264 268 292	1365945051842
SPT(16)	2491587605713600003	0 4 24 60 96 114 124 126 154 156 166 184 220 256 276 280	1713855509576