Prime p₀= 951317991288418727 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 58 2 28 2 34 2 28 2 22 2 (?)
a_n: 0 2 24 26 84 86 114 116 150 152 180 182 204 206
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: 206
Found by: Spectrum
db: batch=76, k=14, 22 58 28 34 28 22

SPT(13)	951317302671384629	0 84 114 162 192 210 222 234 252 282 330 360 444	-688617034098
SPT(16)	951317701792794527	0 14 44 60 80 90 92 102 104 114 116 126 146 162 192 206	-289495624200
SPT(16)	951317765273552293	0 40 70 78 100 130 154 156 178 180 204 234 256 264 294 334	-226014866434
STPT(10)	951317856273726047	0 2 30 32 120 122 210 212 240 242	-135014692680
SPT(16)	951317882856317087	0 14 20 60 62 74 114 140 144 170 210 222 224 264 270 284	-108432101640
STPT(10)	951317894410874759	0 2 18 20 30 32 42 44 60 62	-96877543968
SPT(16)	951318145853396957	0 12 20 26 30 56 62 114 122 174 180 206 210 216 224 236	154564978230
SPT(16)	951318717896224751	0 6 66 72 146 188 206 272 276 342 360 402 476 482 542 548	726607806024
STPT(10)	951318722040665357	0 2 30 32 42 44 54 56 84 86	730752246630
STPT(12)	951318832944697937	0 2 12 14 24 26 30 32 42 44 54 56	841656279210
STPT(12)	951318876421625477	0 2 42 44 84 86 150 152 192 194 234 236	885133206750