Prime p₀= 2787663584803134131 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 82 2 16 2 136 2 82 2 4 2 (?)
a_n: 0 2 6 8 90 92 108 110 246 248 330 332 336 338
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: 338
Found by: JayPi
db: batch=82, k=14, 4 82 16 136 82 4

SPT(16)	2787661736792649637	0 4 12 40 46 70 114 120 166 172 216 240 246 274 282 286	-1848010484494
STPT(10)	2787661895773967579	0 2 48 50 90 92 132 134 180 182	-1689029166552
STPT(10)	2787661993467475211	0 2 6 8 48 50 90 92 96 98	-1591335658920
SPT(16)	2787662674529754839	0 12 20 60 90 108 138 188 192 242 272 290 320 360 368 380	-910273379292
STPT(10)	2787662783300290307	0 2 24 26 42 44 60 62 84 86	-801502843824
STPT(10)	2787663141493757621	0 2 6 8 48 50 90 92 96 98	-443309376510
STPT(10)	2787663696863175197	0 2 12 14 42 44 72 74 84 86	112060041066
SPT(16)	2787663750118707403	0 28 138 150 154 160 168 180 208 220 228 234 238 250 360 388	165315573272
SPT(16)	2787664004230329053	0 18 20 44 48 60 78 170 174 266 284 296 300 324 326 344	419427194922
SPT(16)	2787664128320567009	0 24 134 138 152 164 192 222 290 320 348 360 374 378 488 512	543517432878
SPT(16)	2787664255087270253	0 56 60 128 134 204 248 258 326 336 380 450 456 524 528 584	670284136122