Prime p₀= 1337446206563363801 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 64 2 58 2 28 2 40 2 40 2 (?)
a_n: 0 2 60 62 126 128 186 188 216 218 258 260 300 302
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: Theadalus
db: batch=77, k=14, 58 64 58 28 40 40

SPT(16)	1337444892568543147	0 4 12 42 70 72 82 96 160 174 184 186 214 244 252 256	-1313994820654
SPT(16)	1337445067672898507	0 26 36 66 120 122 152 186 200 234 264 266 320 350 360 386	-1138890465294
STPT(10)	1337445227733254609	0 2 12 14 30 32 48 50 60 62	-978830109192
STPT(10)	1337445233040431087	0 2 42 44 72 74 102 104 144 146	-973522932714
SPT(16)	1337445599273195131	0 102 142 186 196 198 210 250 258 298 310 312 322 366 406 508	-607290168670
STPT(10)	1337445781995854891	0 2 6 8 48 50 90 92 96 98	-424567508910
SPT(16)	1337446368813693401	0 18 32 48 90 102 162 198 230 266 326 338 380 396 410 428	162250329600
STPT(10)	1337446396120065599	0 2 18 20 30 32 42 44 60 62	189556701798
SPT(16)	1337446505906700571	0 16 28 46 72 100 106 148 210 252 258 286 312 330 342 358	299343336770
SPT(16)	1337446981553922049	0 10 18 30 88 100 142 172 198 228 270 282 340 352 360 370	774990558248
SPT(16)	1337447004480211931	0 20 38 48 62 98 108 116 252 260 270 306 320 330 348 368	797916848130