Prime p₀= 2565701113084870091 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 28 2 40 2 76 2 10 2 70 2 (?)
a_n: 0 2 6 8 36 38 78 80 156 158 168 170 240 242
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: 242
Found by: JohnMD
db: batch=82, k=14, 4 28 40 76 10 70

SPT(16)	2565699495975404059	0 18 24 90 102 144 174 190 192 208 238 280 292 358 364 382	-1617109466032
SPT(16)	2565699727129444079	0 20 32 38 48 80 98 122 150 174 192 224 234 240 252 272	-1385955426012
SPT(18)	2565700085820393101	0 26 32 38 42 56 66 68 116 132 180 182 192 206 210 216 222 248	-1027264476990
SPT(16)	2565700565823628967	0 6 24 26 60 96 122 132 164 174 200 236 270 272 290 296	-547261241124
SPT(16)	2565700973395314613	0 28 34 78 108 136 166 196 228 258 288 316 346 390 396 424	-139689555478
STPT(10)	2565701024384170961	0 2 36 38 78 80 120 122 156 158	-88700699130
SPT(16)	2565701529264972437	0 20 50 96 140 170 210 216 296 302 342 372 416 462 492 512	416180102346
SPT(16)	2565701537335209887	0 6 12 60 120 132 174 194 252 272 314 326 386 434 440 446	424250339796
SPT(16)	2565702027044933311	0 16 28 30 126 138 150 156 160 166 178 190 286 288 300 316	913960063220
STPT(10)	2565702253399758791	0 2 48 50 108 110 168 170 216 218	1140314888700
SPT(16)	2565702689516292353	0 44 56 80 126 164 186 198 266 278 300 338 384 408 420 464	1576431422262