Prime p₀= 36057870016923641 starts a Symmetric tuple of 14 consecutive primes (SPT).
d_n: 0 12 6 42 36 20 6 4 6 20 36 42 6 12 (?)
a_n: 0 12 18 60 96 116 122 126 132 152 188 230 236 248
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: 248
Found by: Cruncher Pete
db: batch=65, k=14, 12 6 42 36 20 6 4

SPT(14)	36057851379757499	0 32 140 162 174 182 200 204 222 230 242 264 372 404	-18637166142
SPT(14)	36057853546777633	0 46 60 70 88 96 138 148 190 198 216 226 240 286	-16470146008
SPT(14)	36057856534978921	0 40 42 90 102 118 130 210 222 238 250 298 300 340	-13481944720
SPT(14)	36057858391019653	0 6 48 60 66 84 118 126 160 178 184 196 238 244	-11625903988
SPT(14)	36057859899603929	0 14 30 32 38 78 102 140 164 204 210 212 228 242	-10117319712
SPT(14)	36057867978603529	0 4 10 28 90 154 160 168 174 238 300 318 324 328	-2038320112
TPT(12)	36057870077922419	0 2 72 74 138 140 150 152 192 194 240 242	60998778
SPT(14)	36057873593614703	0 24 26 80 96 120 150 164 194 218 234 288 290 314	3576691062
STPT(10)	36057887570864189	0 2 30 32 60 62 90 92 120 122	17553940548
TPT(12)	36057889439376419	0 2 60 62 102 104 108 110 180 182 198 200	19422452778
SPT(14)	36057889809570533	0 6 20 38 56 78 90 164 176 198 216 234 248 254	19792646892