Prime p₀= 2257328523365247797 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 12 14 58 42 6 20 114 34 114 20 6 42 58 14 12 (?)
a_n: 0 12 26 84 126 132 152 266 300 414 434 440 482 540 554 566
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: 566
Found by: Euphoriabuzz
db: batch=81, k=16, 12 14 58 42 6 20 114 34

SPT(16)	2257327554730209887	0 60 80 92 122 126 144 162 164 182 200 204 234 246 266 326	-968635037910
SPT(16)	2257327860082810061	0 50 56 72 108 128 158 182 186 210 240 260 296 312 318 368	-663282437736
STPT(10)	2257327950775628741	0 2 6 8 48 50 90 92 96 98	-572589619056
SPT(16)	2257328223558123181	0 16 36 70 78 138 142 148 180 186 190 250 258 292 312 328	-299807124616
STPT(10)	2257328315024476667	0 2 30 32 42 44 54 56 84 86	-208340771130
SPT(16)	2257328491497689431	0 28 72 76 82 100 112 136 222 246 258 276 282 286 330 358	-31867558366
SPT(16)	2257328871023364991	0 10 52 102 132 166 178 180 208 210 222 256 286 336 378 388	347658117194
STPT(10)	2257328995576002251	0 2 36 38 78 80 120 122 156 158	472210754454
SPT(16)	2257329324569558441	0 12 20 26 90 108 210 236 252 278 380 398 462 468 476 488	801204310644
SPT(16)	2257329513734120143	0 6 36 64 70 84 90 106 138 154 160 174 180 208 238 244	990368872346
SPT(16)	2257329869139595667	0 26 62 72 110 152 170 222 260 312 330 372 410 420 456 482	1345774347870