Prime p₀= 820181099959634291 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 76 2 40 2 34 2 22 2 94 2 (?)
a_n: 0 2 60 62 138 140 180 182 216 218 240 242 336 338
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: Theadalus
db: batch=73, k=14, 58 76 40 34 22 94

SPT(16)	820180355478913073	0 8 66 84 86 120 170 186 218 234 284 318 320 338 396 404	-744480721218
STPT(10)	820180427376703241	0 2 36 38 78 80 120 122 156 158	-672582931050
STPT(10)	820180482264042041	0 2 6 8 18 20 30 32 36 38	-617695592250
SPT(16)	820180726021794899	0 54 62 72 90 102 188 212 240 264 350 362 380 390 398 452	-373937839392
STPT(10)	820180772109967901	0 2 6 8 48 50 90 92 96 98	-327849666390
STPT(12)	820180864842102299	0 2 18 20 42 44 198 200 222 224 240 242	-235117531992
STPT(10)	820181193152396861	0 2 30 32 78 80 126 128 156 158	93192762570
TPT(14)	820181582476253951	0 2 18 20 90 92 156 158 186 188 228 230 246 248	482516619660
SPT(16)	820181718495681371	0 18 20 32 86 102 128 156 272 300 326 342 396 408 410 428	618536047080
STPT(10)	820182141401112689	0 2 42 44 90 92 138 140 180 182	1041441478398
SPT(16)	820182430820880377	0 12 60 74 90 104 126 150 176 200 222 236 252 266 314 326	1330861246086