Prime p₀= 2141269363729290719 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 58 2 4 2 58 2 10 2 16 2 (?)
a_n: 0 2 12 14 72 74 78 80 138 140 150 152 168 170
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: 170
Found by: [SG-2W]Kurzer
db: batch=80, k=14, 10 58 4 58 10 16

TPT(14)	2141268017997214031	0 2 48 50 78 80 120 122 186 188 210 212 246 248	-1345732076688
SPT(16)	2141268087092088293	0 6 20 50 54 80 86 114 146 174 180 206 210 240 254 260	-1276637202426
SPT(16)	2141269078311608717	0 2 30 50 62 66 80 146 156 222 236 240 252 272 300 302	-285417682002
SPT(16)	2141269252371978887	0 2 42 120 152 222 236 272 330 366 380 450 482 560 600 602	-111357311832
SPT(16)	2141269298877010361	0 48 126 272 278 308 330 342 386 398 420 450 456 602 680 728	-64852280358
SPT(16)	2141269346412486427	0 34 82 124 126 166 180 186 190 196 210 250 252 294 342 376	-17316804292
STPT(12)	2141269363729290719	0 2 12 14 72 74 78 80 138 140 150 152	0
STPT(10)	2141269419262894889	0 2 48 50 90 92 132 134 180 182	55533604170
STPT(12)	2141269704784472189	0 2 30 32 42 44 90 92 102 104 132 134	341055181470
STPT(10)	2141269814883449177	0 2 12 14 72 74 132 134 144 146	451154158458
STPT(10)	2141270513028269039	0 2 18 20 30 32 42 44 60 62	1149298978320