Prime p₀= 2164237658413044677 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 328 2 4 2 22 2 16 2 76 2 (?)
a_n: 0 2 84 86 414 416 420 422 444 446 462 464 540 542
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: 542
Found by: Landjunge
db: batch=81, k=14, 82 328 4 22 16 76

SPT(18)	2164235986412942747	0 12 56 74 86 90 96 116 132 194 210 230 236 240 252 270 314 326	-1672000101930
SPT(16)	2164236390234771269	0 62 110 204 260 294 300 344 348 392 398 432 488 582 630 692	-1268178273408
STPT(10)	2164236433141370447	0 2 30 32 72 74 114 116 144 146	-1225271674230
SPT(18)	2164237298434204303	0 10 24 30 34 36 48 66 148 156 238 256 268 270 274 280 294 304	-359978840374
SPT(16)	2164237439661472333	0 70 90 124 138 160 184 226 228 270 294 316 330 364 384 454	-218751572344
TPT(14)	2164237498938260561	0 2 90 92 126 128 336 338 408 410 420 422 558 560	-159474784116
SPT(16)	2164237666682699737	0 6 30 42 52 82 90 100 192 202 210 240 250 262 286 292	8269655060
STPT(10)	2164238047892338469	0 2 42 44 60 62 78 80 120 122	389479293792
STPT(10)	2164238113061650817	0 2 42 44 72 74 102 104 144 146	454648606140
SPT(16)	2164238320741624571	0 6 8 20 26 42 90 162 266 338 386 402 408 420 422 428	662328579894
SPT(16)	2164238353691060707	0 16 102 154 184 196 240 246 250 256 300 312 342 394 480 496	695278016030