Prime p₀= 2567345687852807429 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 28 2 34 2 58 2 10 2 16 2 (?)
a_n: 0 2 12 14 42 44 78 80 138 140 150 152 168 170
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: 170
Found by: JayPi
db: batch=82, k=14, 10 28 34 58 10 16

SPT(16)	2567344520423123999	0 24 84 134 162 192 194 210 242 258 260 290 318 368 428 452	-1167429683430
TPT(14)	2567345035184277197	0 2 24 26 120 122 174 176 180 182 192 194 222 224	-652668530232
STPT(10)	2567345071820400197	0 2 60 62 72 74 84 86 144 146	-616032407232
SPT(16)	2567345125083441601	0 12 16 22 28 40 42 52 126 136 138 150 156 162 166 178	-562769365828
SPT(16)	2567345146556530001	0 2 6 12 30 48 72 90 98 116 140 158 176 182 186 188	-541296277428
SPT(16)	2567345356155326627	0 12 30 66 140 152 206 234 242 270 324 336 410 446 464 476	-331697480802
STPT(10)	2567345845382271377	0 2 30 32 72 74 114 116 144 146	157529463948
SPT(16)	2567346169625179529	0 12 14 48 60 72 74 104 108 138 140 152 164 198 200 212	481772372100
STPT(10)	2567346326509601627	0 2 12 14 42 44 72 74 84 86	638656794198
SPT(16)	2567346959022721081	0 30 42 48 82 120 136 150 208 222 238 276 310 316 328 358	1271169913652
STPT(10)	2567347275383579831	0 2 6 8 18 20 30 32 36 38	1587530772402