Prime p₀= 1165599059077795577 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 142 2 34 2 70 2 40 2 4 2 40 2 (?)
a_n: 0 2 144 146 180 182 252 254 294 296 300 302 342 344
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: 344
Found by: Megacruncher
db: batch=77, k=14, 142 34 70 40 4 40

SPT(16)	1165598632029263441	0 32 48 66 122 188 210 218 240 248 270 336 392 410 426 458	-427048532136
TPT(14)	1165598728445121821	0 2 6 8 30 32 90 92 168 170 198 200 240 242	-330632673756
STPT(10)	1165598844900068399	0 2 42 44 60 62 78 80 120 122	-214177727178
SPT(16)	1165598931315695923	0 18 30 96 124 186 204 216 238 250 268 330 358 424 436 454	-127762099654
STPT(10)	1165598956950167651	0 2 6 8 18 20 30 32 36 38	-102127627926
SPT(16)	1165599051949083407	0 62 122 140 162 192 200 234 242 276 284 314 336 354 414 476	-7128712170
TPT(16)	1165599420981355667	0 2 24 26 84 86 102 104 150 152 192 194 222 224 324 326	361903560090
STPT(10)	1165599637668870161	0 2 6 8 18 20 30 32 36 38	578591074584
STPT(10)	1165600184858245349	0 2 48 50 90 92 132 134 180 182	1125780449772
SPT(16)	1165600386299539219	0 12 42 60 78 120 142 144 208 210 232 274 292 310 340 352	1327221743642
SPT(16)	1165600972557915253	0 6 40 66 120 138 148 180 304 336 346 364 418 444 478 484	1913480119676