Prime p₀= 2562111276625950611 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 42 30 14 4 122 4 24 68 24 4 122 4 14 30 42 (?)
a_n: 0 42 72 86 90 212 216 240 308 332 336 458 462 476 506 548
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: 548
Found by: Penguin
db: batch=82, k=16, 42 30 14 4 122 4 24 68

SPT(16)	2562109223202045701	0 38 48 78 86 90 92 98 150 156 158 162 170 200 210 248	-2053423904910
SPT(16)	2562109531643749151	0 8 30 38 42 78 122 138 182 198 242 278 282 290 312 320	-1744982201460
STPT(12)	2562109653188216777	0 2 60 62 84 86 90 92 114 116 174 176	-1623437733834
SPT(16)	2562110166295754653	0 24 90 106 138 168 204 216 238 250 286 316 348 364 430 454	-1110330195958
SPT(16)	2562110349564458321	0 30 68 72 80 110 126 128 210 212 228 258 266 270 308 338	-927061492290
STPT(10)	2562110956780341467	0 2 54 56 72 74 90 92 144 146	-319845609144
SPT(16)	2562111303185794219	0 10 60 82 142 150 198 228 304 334 382 390 450 472 522 532	26559843608
STPT(10)	2562111563223635231	0 2 6 8 48 50 90 92 96 98	286597684620
SPT(16)	2562111686741587823	0 20 24 30 98 104 126 138 266 278 300 306 374 380 384 404	410115637212
TPT(14)	2562111814787875277	0 2 54 56 90 92 180 182 210 212 264 266 300 302	538161924666
STPT(12)	2562111832704621479	0 2 18 20 42 44 78 80 102 104 120 122	556078670868