Prime p₀= 2815408227261959321 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 142 2 64 2 70 2 28 2 10 2 (?)
a_n: 0 2 66 68 210 212 276 278 348 350 378 380 390 392
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: 392
Found by: JayPi
db: batch=82, k=14, 64 142 64 70 28 10

SPT(16)	2815406015279288051	0 20 60 62 90 108 132 180 188 236 260 278 306 308 348 368	-2211982671270
SPT(16)	2815406031236583523	0 40 76 78 118 138 156 226 228 298 316 336 376 378 414 454	-2196025375798
SPT(16)	2815406138953364557	0 12 34 54 60 96 186 216 220 250 340 376 382 402 424 436	-2088308594764
STPT(10)	2815406361049201847	0 2 30 32 72 74 114 116 144 146	-1866212757474
STPT(10)	2815406414512755797	0 2 24 26 42 44 60 62 84 86	-1812749203524
SPT(16)	2815406725622686361	0 138 158 162 168 182 188 216 272 300 306 320 326 330 350 488	-1501639272960
SPT(16)	2815408402981997057	0 26 42 60 86 114 126 140 396 410 422 450 476 494 510 536	175720037736
STPT(10)	2815409032045468679	0 2 42 44 60 62 78 80 120 122	804783509358
SPT(16)	2815409291132238649	0 10 34 78 84 88 120 144 244 268 300 304 310 354 378 388	1063870279328
SPT(16)	2815409403592938137	0 20 66 72 122 146 222 230 276 284 360 384 434 440 486 506	1176330978816
SPT(16)	2815409973926039543	0 6 20 50 60 74 128 138 176 186 240 254 264 294 308 314	1746664080222