Prime p₀= 781021169051465621 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 136 2 130 2 4 2 82 2 4 2 10 2 (?)
a_n: 0 2 138 140 270 272 276 278 360 362 366 368 378 380
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: 380
Found by: [SG]steini
db: batch=73, k=14, 136 130 4 82 4 10

SPT(16)	781020218395678801	0 16 70 72 78 102 108 126 172 190 196 220 226 228 282 298	-950655786820
STPT(10)	781020237065258171	0 2 36 38 78 80 120 122 156 158	-931986207450
SPT(16)	781020278705672359	0 22 30 58 60 100 142 148 162 168 210 250 252 280 288 310	-890345793262
STPT(10)	781020454979966867	0 2 12 14 42 44 72 74 84 86	-714071498754
STPT(10)	781020461414334257	0 2 30 32 42 44 54 56 84 86	-707637131364
SPT(16)	781020809503999357	0 10 12 16 24 34 54 72 94 112 132 142 150 154 156 166	-359547466264
SPT(16)	781021773987100231	0 10 22 36 46 78 126 148 210 232 280 312 322 336 348 358	604935634610
STPT(10)	781021806133798121	0 2 6 8 48 50 90 92 96 98	637082332500
SPT(16)	781021856250863377	0 10 30 66 82 96 142 160 216 234 280 294 310 346 366 376	687199397756
SPT(16)	781022152508787197	0 50 66 84 114 156 182 204 242 264 290 332 362 380 396 446	983457321576
STPT(10)	781022334295900979	0 2 18 20 60 62 102 104 120 122	1165244435358