Prime p₀= 924138409588462457 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 82 2 58 2 34 2 28 2 22 2 (?)
a_n: 0 2 30 32 114 116 174 176 210 212 240 242 264 266
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: 266
Found by: Theadalus
db: batch=76, k=14, 28 82 58 34 28 22

SPT(16)	924138104780476631	0 12 30 36 38 78 80 90 128 138 140 180 182 188 206 218	-304807985826
SPT(16)	924138177762450517	0 6 60 72 136 150 172 202 210 240 262 276 340 352 406 412	-231826011940
SPT(16)	924138189836146763	0 20 36 48 66 78 86 104 150 168 176 188 206 218 234 254	-219752315694
STPT(10)	924138251112052157	0 2 30 32 42 44 54 56 84 86	-158476410300
SPT(16)	924138276539955131	0 6 12 26 30 42 56 68 90 102 116 128 132 146 152 158	-133048507326
SPT(16)	924138280965234733	0 6 24 28 30 66 76 84 160 168 178 214 216 220 238 244	-128623227724
TPT(14)	924138447050439791	0 2 30 32 78 80 210 212 216 218 240 242 288 290	37461977334
STPT(10)	924138742955567507	0 2 30 32 42 44 54 56 84 86	333367105050
STPT(10)	924138854599300799	0 2 18 20 30 32 42 44 60 62	445010838342
STPT(10)	924138929869600769	0 2 18 20 30 32 42 44 60 62	520281138312
STPT(10)	924139265824171091	0 2 30 32 78 80 126 128 156 158	856235708634