Prime p₀= 2051671893162067877 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 34 2 70 2 70 2 124 2 22 2 (?)
a_n: 0 2 84 86 120 122 192 194 264 266 390 392 414 416
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: 416
Found by: Landjunge
db: batch=80, k=14, 82 34 70 70 124 22

STPT(10)	2051668962358426391	0 2 30 32 78 80 126 128 156 158	-2930803641486
STPT(10)	2051669021058742649	0 2 48 50 90 92 132 134 180 182	-2872103325228
SPT(16)	2051669183208055057	0 10 30 34 100 106 124 150 166 192 210 216 282 286 306 316	-2709954012820
SPT(16)	2051670001912074133	0 6 10 24 64 76 78 90 94 106 108 120 160 174 178 184	-1891249993744
TPT(14)	2051670894494308889	0 2 18 20 48 50 222 224 282 284 300 302 312 314	-998667758988
STPT(10)	2051671599954350741	0 2 6 8 48 50 90 92 96 98	-293207717136
TPT(14)	2051671893295182911	0 2 18 20 126 128 156 158 186 188 258 260 306 308	133115034
TPT(14)	2051672015766699251	0 2 30 32 48 50 78 80 126 128 156 158 336 338	122604631374
STPT(10)	2051672024654365427	0 2 30 32 42 44 54 56 84 86	131492297550
SPT(16)	2051672193184803307	0 42 46 76 96 100 130 184 252 306 336 340 360 390 394 436	300022735430
SPT(16)	2051672288283900181	0 30 48 72 82 100 120 130 198 208 228 246 256 280 298 328	395121832304