Prime p₀= 253164976659286123 starts a Symmetric tuple of 14 consecutive primes (SPT).
d_n: 0 4 2 48 6 24 10 26 10 24 6 48 2 4 (?)
a_n: 0 4 6 54 60 84 94 120 130 154 160 208 210 214
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: 214
Found by: desktop64
db: batch=69, k=14, 4 2 48 6 24 10 26

TPT(12)	253164876501410189	0 2 30 32 108 110 120 122 138 140 162 164	-100157875934
SPT(14)	253164923809463411	0 12 18 36 56 62 72 116 126 132 152 170 176 188	-52849822712
TPT(12)	253164932097590057	0 2 24 26 30 32 54 56 72 74 114 116	-44561696066
SPT(14)	253164941301747281	0 50 56 60 92 108 122 126 140 156 188 192 198 248	-35357538842
SPT(14)	253164949344019441	0 42 46 66 70 100 156 166 222 252 256 276 280 322	-27315266682
SPT(14)	253164953516668927	0 4 42 54 82 84 96 130 142 144 172 184 222 226	-23142617196
SPT(14)	253164997358387899	0 30 42 58 78 82 114 148 180 184 204 220 232 262	20699101776
SPT(14)	253165005377009963	0 30 48 80 90 98 108 146 156 164 174 206 224 254	28717723840
SPT(14)	253165009092290237	0 12 42 54 60 92 104 180 192 224 230 242 272 284	32433004114
SPT(14)	253165019573865481	0 10 70 106 108 112 162 166 216 220 222 258 318 328	42914579358
TPT(12)	253165021630123037	0 2 12 14 30 32 54 56 162 164 204 206	44970836914