Prime p₀= 1317125478265374131 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 136 2 10 2 46 2 28 2 40 2 (?)
a_n: 0 2 30 32 168 170 180 182 228 230 258 260 300 302
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: 302
Found by: emoga
db: batch=77, k=14, 28 136 10 46 28 40

SPT(16)	1317123386735644721	0 60 72 116 122 140 146 182 276 312 318 336 342 386 398 458	-2091529729410
STPT(10)	1317123419874161069	0 2 18 20 60 62 102 104 120 122	-2058391213062
SPT(16)	1317123816865189181	0 32 38 56 66 78 80 116 132 168 170 182 192 210 216 248	-1661400184950
STPT(10)	1317123971315656919	0 2 48 50 60 62 72 74 120 122	-1506949717212
SPT(16)	1317124640285014733	0 30 44 68 98 104 126 204 230 308 330 336 366 390 404 434	-837980359398
SPT(20)	1317125014527524357	0 36 56 80 86 152 156 162 176 206 240 270 284 290 294 360 366 390 410 446	-463737849774
SPT(16)	1317125599963250417	0 14 20 26 36 42 62 72 74 84 104 110 120 126 132 146	121697876286
SPT(16)	1317126071828901787	0 6 22 34 82 120 124 126 160 162 166 204 252 264 280 286	593563527656
SPT(16)	1317126199885097111	0 6 30 80 90 108 156 170 276 290 338 356 366 416 440 446	721619722980
SPT(18)	1317126211526095057	0 10 90 124 196 216 306 336 390 400 454 484 574 594 666 700 780 790	733260720926
SPT(16)	1317126534274079167	0 4 22 66 90 100 132 172 174 214 246 256 280 324 342 346	1056008705036