Prime p₀= 4387503687291773413 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 30 16 8 24 18 58 2 22 2 58 18 24 8 16 30 (?)
a_n: 0 30 46 54 78 96 154 156 178 180 238 256 280 288 304 334
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: 334
Found by: [SG]KidDoesCrunch
db: batch=85, k=16, 30 16 8 24 18 58 2 22

SPT(16)	4387500744636647089	0 70 88 114 148 168 180 190 222 232 244 264 298 324 342 412	-2942655126324
STPT(10)	4387500978425261777	0 2 90 92 150 152 210 212 300 302	-2708866511636
SPT(16)	4387501228682631863	0 20 30 44 56 90 96 138 146 188 194 228 240 254 264 284	-2458609141550
STPT(10)	4387501900420013729	0 2 48 50 90 92 132 134 180 182	-1786871759684
STPT(10)	4387502862469386761	0 2 6 8 48 50 90 92 96 98	-824822386652
STPT(10)	4387503494646759959	0 2 42 44 90 92 138 140 180 182	-192645013454
SPT(16)	4387503732681102893	0 90 104 114 116 150 168 234 290 356 374 408 410 420 434 524	45389329480
SPT(16)	4387504089218955751	0 12 16 28 36 40 46 48 70 72 78 82 90 102 106 118	401927182338
STPT(10)	4387504623411344387	0 2 30 32 42 44 54 56 84 86	936119570974
STPT(10)	4387505142996338681	0 2 36 38 108 110 180 182 216 218	1455704565268
SPT(16)	4387505181254518483	0 6 24 28 30 94 144 196 198 250 300 364 366 370 388 394	1493962745070