Prime p₀= 2066263109998882451 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 28 2 100 2 70 2 118 2 124 2 (?)
a_n: 0 2 66 68 96 98 198 200 270 272 390 392 516 518
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: 518
Found by: Cruncher Pete
db: batch=80, k=14, 64 28 100 70 118 124

SPT(16)	2066261311693845397	0 4 6 22 70 82 84 106 150 172 174 186 234 250 252 256	-1798305037054
SPT(16)	2066261489121049543	0 4 46 66 70 180 214 250 294 330 364 474 478 498 540 544	-1620877832908
SPT(16)	2066261927232121351	0 6 36 46 66 78 88 126 172 210 220 232 252 262 292 298	-1182766761100
SPT(16)	2066262754424289373	0 30 40 54 66 96 148 150 154 156 208 238 250 264 274 304	-355574593078
TPT(14)	2066262826736801981	0 2 30 32 78 80 138 140 288 290 318 320 330 332	-283262080470
STPT(10)	2066263037385239447	0 2 30 32 42 44 54 56 84 86	-72613643004
SPT(16)	2066263122633006883	0 10 24 34 46 48 66 70 84 88 106 108 120 130 144 154	12634124432
SPT(16)	2066263137673277827	0 34 36 60 76 96 126 174 406 454 484 504 520 544 546 580	27674395376
SPT(16)	2066263573239170177	0 54 66 80 116 134 140 146 264 270 276 294 330 344 356 410	463240287726
STPT(10)	2066263595379655337	0 2 12 14 42 44 72 74 84 86	485380772886
SPT(16)	2066264272833162763	0 30 34 64 100 210 268 270 298 300 358 468 504 534 538 568	1162834280312