Prime p₀= 1007717651236390121 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 46 2 58 2 82 2 28 2 34 2 (?)
a_n: 0 2 18 20 66 68 126 128 210 212 240 242 276 278
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: 278
Found by: stoneageman
db: batch=76, k=14, 16 46 58 82 28 34

SPT(13)	1007716893479867717	0 12 24 42 84 90 132 174 180 222 240 252 264	-757756522404
STPT(10)	1007716905897984197	0 2 24 26 42 44 60 62 84 86	-745338405924
SPT(16)	1007716973908890733	0 34 48 66 70 160 178 190 234 246 264 354 358 376 390 424	-677327499388
SPT(16)	1007717286738030023	0 8 30 60 86 96 114 126 128 140 158 168 194 224 246 254	-364498360098
SPT(16)	1007717376935046697	0 6 12 22 34 52 124 150 166 192 264 282 294 304 310 316	-274301343424
SPT(16)	1007717479681141597	0 12 36 46 96 124 132 162 214 244 252 280 330 340 364 376	-171555248524
SPT(16)	1007717954486370947	0 2 26 72 80 102 120 180 182 242 260 282 290 336 360 362	303249980826
SPT(16)	1007718004616138917	0 10 22 40 52 76 90 96 136 142 156 180 192 210 222 232	353379748796
SPT(16)	1007718067898335721	0 6 36 42 72 110 146 152 156 162 198 236 266 272 302 308	416661945600
STPT(10)	1007718125615521421	0 2 6 8 48 50 90 92 96 98	474379131300
TPT(14)	1007718238689172271	0 2 126 128 186 188 258 260 330 332 450 452 468 470	587452782150