Prime p₀= 527641321549992709 starts a Symmetric tuple of 14 consecutive primes (SPT).
d_n: 0 42 48 24 6 12 22 14 22 12 6 24 48 42 (?)
a_n: 0 42 90 114 120 132 154 168 190 202 208 232 280 322
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 322
Found by: gemini8
db: batch=71, k=14, 42 48 24 6 12 22 14

SPT(16)	527641277481945331	0 22 40 70 130 196 220 222 370 372 396 462 522 552 570 592	-44068047378
SPT(14)	527641280424262931	0 12 20 62 66 146 180 182 216 296 300 342 350 362	-41125729778
SPT(16)	527641285428365557	0 4 10 30 64 72 102 114 142 154 184 192 226 246 252 256	-36121627152
SPT(14)	527641303920478301	0 8 30 72 80 140 152 168 180 240 248 290 312 320	-17629514408
TPT(12)	527641311792788951	0 2 36 38 258 260 288 290 378 380 426 428	-9757203758
SPT(14)	527641313458632421	0 28 48 102 112 126 130 138 142 156 166 220 240 268	-8091360288
SPT(14)	527641333457438237	0 42 50 60 66 102 116 126 140 176 182 192 200 242	11907445528
SPT(14)	527641349375407769	0 14 24 50 60 78 104 138 164 182 192 218 228 242	27825415060
TPT(12)	527641388972874731	0 2 90 92 126 128 198 200 258 260 300 302	67422882022
SPT(14)	527641416332688253	0 24 36 78 100 136 154 180 198 234 256 298 310 334	94782695544
SPT(14)	527641423817085197	0 36 42 54 90 116 176 180 240 266 302 314 320 356	102267092488