Prime p₀= 391468803885469559 starts a Symmetric tuple of 14 consecutive primes (SPT).
d_n: 0 32 30 6 4 18 44 4 44 18 4 6 30 32 (?)
a_n: 0 32 62 68 72 90 134 138 182 200 204 210 240 272
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: 272
Found by: Cruncher Pete
db: batch=70, k=14, 32 30 6 4 18 44 4

SPT(14)	391468708776732109	0 12 22 40 90 118 120 130 132 160 210 228 238 250	-95108737450
SPT(14)	391468742114707381	0 18 66 90 102 106 132 166 192 196 208 232 280 298	-61770762178
SPT(16)	391468767713337019	0 34 60 82 102 118 132 168 214 250 264 280 300 322 348 382	-36172132540
SPT(14)	391468771079312713	0 10 24 70 100 114 124 150 160 174 204 250 264 274	-32806156846
TPT(12)	391468793835500189	0 2 72 74 180 182 252 254 342 344 462 464	-10049969370
SPT(14)	391468796334804911	0 30 42 72 86 210 228 230 248 372 386 416 428 458	-7550664648
SPT(14)	391468825706331631	0 10 18 46 88 166 180 208 222 300 342 370 378 388	21820862072
SPT(14)	391468854504913091	0 2 12 20 30 48 56 132 140 158 168 176 186 188	50619443532
TPT(12)	391468856553704297	0 2 42 44 54 56 84 86 90 92 174 176	52668234738
TPT(12)	391468865602000451	0 2 66 68 108 110 126 128 150 152 168 170	61716530892
SPT(14)	391468867236963011	0 62 90 96 108 126 132 146 152 170 182 188 216 278	63351493452