Prime p₀= 456495950068275319 starts a Symmetric tuple of 14 consecutive primes (SPT).
d_n: 0 12 12 18 28 72 2 76 2 72 28 18 12 12 (?)
a_n: 0 12 24 42 70 142 144 220 222 294 322 340 352 364
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: 364
Found by: Cruncher Pete
db: batch=70, k=14, 12 12 18 28 72 2 76

SPT(14)	456495883897150729	0 48 60 64 78 112 150 172 210 244 258 262 274 322	-66171124590
SPT(14)	456495892889636651	0 2 8 30 50 90 98 120 128 168 188 210 216 218	-57178638668
TPT(12)	456495917887406699	0 2 12 14 42 44 108 110 120 122 168 170	-32180868620
SPT(14)	456495919063603213	0 54 58 78 84 88 106 138 156 160 166 186 190 244	-31004672106
SPT(14)	456495924411748973	0 20 30 96 114 140 156 164 180 206 224 290 300 320	-25656526346
SPT(14)	456495939776967791	0 30 42 56 86 156 162 296 302 372 402 416 428 458	-10291307528
TPT(12)	456495996109356869	0 2 72 74 162 164 198 200 222 224 402 404	46041081550
SPT(16)	456496010758399459	0 18 42 102 178 180 210 220 240 250 280 282 358 418 442 460	60690124140
SPT(14)	456496053442264669	0 58 108 120 124 142 144 148 150 168 172 184 234 292	103373989350
SPT(16)	456496085385199819	0 18 22 40 112 130 138 144 208 214 222 240 312 330 334 352	135316924500
SPT(14)	456496092793021153	0 6 28 64 124 130 144 190 204 210 270 306 328 334	142724745834