Prime p₀= 342423588160969933 starts a Symmetric tuple of 14 consecutive primes (SPT).
d_n: 0 36 10 20 10 2 70 50 70 2 10 20 10 36 (?)
a_n: 0 36 46 66 76 78 148 198 268 270 280 300 310 346
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: 346
Found by: Cruncher Pete
db: batch=70, k=14, 36 10 20 10 2 70 50

SPT(14)	342423550551029429	0 54 60 72 74 84 104 108 128 138 140 152 158 212	-37609940504
SPT(14)	342423554738821069	0 10 24 30 42 52 90 94 132 142 154 160 174 184	-33422148864
SPT(14)	342423555003625547	0 20 26 30 50 156 174 176 194 300 320 324 330 350	-33157344386
TPT(12)	342423569149710017	0 2 30 32 90 92 114 116 144 146 294 296	-19011259916
SPT(14)	342423573299282071	0 10 22 60 72 78 108 112 142 148 160 198 210 220	-14861687862
SPT(14)	342423579916227127	0 10 30 52 66 94 112 114 132 160 174 196 216 226	-8244742806
SPT(14)	342423593339685059	0 42 80 104 170 182 192 212 222 234 300 324 362 404	5178715126
SPT(14)	342423606095913481	0 10 28 46 66 76 88 90 102 112 132 150 168 178	17934943548
SPT(14)	342423615933783311	0 2 12 72 90 146 168 200 222 278 296 356 366 368	27772813378
TPT(12)	342423623740453247	0 2 24 26 102 104 144 146 150 152 210 212	35579483314
SPT(14)	342423631456098121	0 12 28 46 72 88 102 196 210 226 252 270 286 298	43295128188