Prime p₀= 811013402528196587 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 76 2 88 2 16 2 112 2 34 2 (?)
a_n: 0 2 24 26 102 104 192 194 210 212 324 326 360 362
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: 362
Found by: amazing
db: batch=73, k=14, 22 76 88 16 112 34

SPT(16)	811012010648801743	0 40 78 90 196 300 304 306 358 360 364 468 574 586 624 664	-1391879394844
TPT(14)	811012175790314339	0 2 18 20 48 50 78 80 210 212 240 242 252 254	-1226737882248
SPT(16)	811012255761288727	0 16 46 84 100 102 112 124 132 144 154 156 172 210 240 256	-1146766907860
SPT(16)	811012454172632053	0 40 84 96 124 130 136 168 226 258 264 270 298 310 354 394	-948355564534
SPT(16)	811012910583204977	0 14 74 84 102 110 204 266 300 362 456 464 482 492 552 566	-491944991610
TPT(14)	811013224093093841	0 2 150 152 276 278 306 308 318 320 360 362 378 380	-178435102746
TPT(14)	811013411483554127	0 2 30 32 102 104 114 116 270 272 312 314 330 332	8955357540
SPT(16)	811013678921789489	0 14 32 42 80 104 122 198 224 300 318 342 380 390 408 422	276393592902
SPT(16)	811013768627241799	0 28 70 88 102 124 142 168 214 240 258 280 294 312 354 382	366099045212
SPT(16)	811014175067942353	0 4 36 96 126 208 216 274 390 448 456 538 568 628 660 664	772539745766
STPT(10)	811014290189762801	0 2 6 8 18 20 30 32 36 38	887661566214