Prime p₀= 1411799826716093849 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 76 2 82 2 16 2 28 2 10 2 (?)
a_n: 0 2 60 62 138 140 222 224 240 242 270 272 282 284
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: 284
Found by: Theadalus
db: batch=78, k=14, 58 76 82 16 28 10

SPT(16)	1411797679618434389	0 72 98 114 128 134 138 158 204 224 228 234 248 264 290 362	-2147097659460
STPT(10)	1411798080745141091	0 2 36 38 78 80 120 122 156 158	-1745970952758
TPT(14)	1411798289044589057	0 2 42 44 54 56 132 134 150 152 204 206 252 254	-1537671504792
STPT(10)	1411799213918763359	0 2 18 20 30 32 42 44 60 62	-612797330490
SPT(16)	1411799284115495741	0 8 42 90 92 102 120 140 180 200 218 228 230 278 312 320	-542600598108
SPT(16)	1411799519422715021	0 20 42 86 120 152 176 240 278 342 366 398 432 476 498 518	-307293378828
SPT(16)	1411799931332305079	0 14 38 74 80 204 224 248 264 288 308 432 438 474 498 512	104616211230
STPT(10)	1411799989418993771	0 2 36 38 78 80 120 122 156 158	162702899922
STPT(10)	1411800102944531351	0 2 6 8 18 20 30 32 36 38	276228437502
SPT(18)	1411800138942614657	0 42 84 132 162 176 224 266 272 294 300 342 390 404 434 482 524 566	312226520808
SPT(16)	1411800538937730631	0 28 42 46 120 148 156 252 286 382 390 418 492 496 510 538	712221636782