Prime p₀= 2531126790076309577 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 14 6 42 18 4 66 2 10 2 66 4 18 42 6 14 (?)
a_n: 0 14 20 62 80 84 150 152 162 164 230 234 252 294 300 314
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: 314
Found by: [SG]ATA-Rolf
db: batch=82, k=16, 14 6 42 18 4 66 2 10

SPT(16)	2531125385469811499	0 20 62 74 110 144 150 152 222 224 230 264 300 312 354 374	-1404606498078
SPT(16)	2531125504852666571	0 2 80 90 128 132 170 182 198 210 248 252 290 300 378 380	-1285223643006
STPT(10)	2531126079033778559	0 2 48 50 90 92 132 134 180 182	-711042531018
TPT(14)	2531126123933342807	0 2 42 44 84 86 102 104 132 134 144 146 222 224	-666142966770
SPT(16)	2531126539634012381	0 42 48 110 132 140 152 162 278 288 300 308 330 392 398 440	-250442297196
STPT(10)	2531126785092126581	0 2 6 8 48 50 90 92 96 98	-4984182996
STPT(10)	2531126924612085221	0 2 30 32 120 122 210 212 240 242	134535775644
SPT(16)	2531127151676136779	0 38 98 104 108 122 132 134 138 140 150 164 168 174 234 272	361599827202
STPT(10)	2531127555628550141	0 2 6 8 48 50 90 92 96 98	765552240564
STPT(10)	2531127664548363887	0 2 30 32 42 44 54 56 84 86	874472054310
SPT(16)	2531127911110751431	0 6 10 48 90 136 156 162 196 202 222 268 310 348 352 358	1121034441854