Prime p₀= 4387486911443466101 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 8 34 20 4 30 14 72 4 72 14 30 4 20 34 8 (?)
a_n: 0 8 42 62 66 96 110 182 186 258 272 302 306 326 360 368
All 16 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 368
Found by: [SG]KidDoesCrunch
db: batch=85, k=16, 8 34 20 4 30 14 72 4

STPT(10)	4387485273221682341	0 2 78 80 108 110 138 140 216 218	-1638221783760
SPT(16)	4387485387551925227	0 6 24 30 44 62 86 126 230 270 294 312 326 332 350 356	-1523891540874
SPT(16)	4387485501048976897	0 42 82 90 124 126 130 132 244 246 250 252 286 294 334 376	-1410394489204
SPT(16)	4387486354764882731	0 36 62 108 216 218 246 300 428 482 510 512 620 666 692 728	-556678583370
SPT(16)	4387486660941566719	0 12 34 60 78 82 154 162 220 228 300 304 322 348 370 382	-250501899382
SPT(16)	4387486754114947393	0 16 66 96 106 124 148 154 180 186 210 228 238 268 318 334	-157328518708
STPT(10)	4387487161550980841	0 2 6 8 48 50 90 92 96 98	250107514740
TPT(14)	4387487644482081239	0 2 60 62 240 242 258 260 270 272 282 284 378 380	733038615138
SPT(16)	4387487660688692099	0 42 60 108 134 192 228 242 270 284 320 378 404 452 470 512	749245225998
SPT(16)	4387487671681225997	0 42 90 92 132 146 186 200 246 260 300 314 354 356 404 446	760237759896
SPT(16)	4387487924777617931	0 38 90 120 126 150 176 182 186 192 218 242 248 278 330 368	1013334151830