Prime p₀= 1258073726603015051 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 166 2 70 2 4 2 130 2 28 2 16 2 (?)
a_n: 0 2 168 170 240 242 246 248 378 380 408 410 426 428
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: 428
Found by: HenkM
db: batch=77, k=14, 166 70 4 130 28 16

SPT(16)	1258072733504077783	0 10 24 28 40 64 66 136 138 208 210 234 246 250 264 274	-993098937268
SPT(16)	1258072907517120619	0 4 30 42 58 64 70 88 204 222 228 234 250 262 288 292	-819085894432
STPT(10)	1258073169466050701	0 2 30 32 78 80 126 128 156 158	-557136964350
STPT(10)	1258073510006114027	0 2 30 32 72 74 114 116 144 146	-216596901024
SPT(16)	1258073602147224649	0 30 40 70 90 112 114 132 202 220 222 244 264 294 304 334	-124455790402
TPT(14)	1258073615593652939	0 2 30 32 42 44 90 92 132 134 168 170 198 200	-111009362112
STPT(10)	1258073904137573189	0 2 18 20 30 32 42 44 60 62	177534558138
SPT(16)	1258073940405349351	0 22 30 58 76 82 142 160 168 186 246 252 270 298 306 328	213802334300
TPT(14)	1258073995753136447	0 2 30 32 54 56 144 146 174 176 222 224 240 242	269150121396
TPT(14)	1258074211323926417	0 2 12 14 120 122 150 152 180 182 210 212 222 224	484720911366
SPT(16)	1258074244292127673	0 28 34 36 90 130 180 204 220 244 294 334 388 390 396 424	517689112622