Prime p₀= 527641313458632421 starts a Symmetric tuple of 14 consecutive primes (SPT).
d_n: 0 28 20 54 10 14 4 8 4 14 10 54 20 28 (?)
a_n: 0 28 48 102 112 126 130 138 142 156 166 220 240 268
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: 268
Found by: gemini8
db: batch=71, k=14, 28 20 54 10 14 4 8

SPT(16)	527641253638082393	0 20 66 80 96 104 120 150 164 194 210 218 234 248 294 314	-59820550028
SPT(16)	527641277481945331	0 22 40 70 130 196 220 222 370 372 396 462 522 552 570 592	-35976687090
SPT(14)	527641280424262931	0 12 20 62 66 146 180 182 216 296 300 342 350 362	-33034369490
SPT(16)	527641285428365557	0 4 10 30 64 72 102 114 142 154 184 192 226 246 252 256	-28030266864
SPT(14)	527641303920478301	0 8 30 72 80 140 152 168 180 240 248 290 312 320	-9538154120
TPT(12)	527641311792788951	0 2 36 38 258 260 288 290 378 380 426 428	-1665843470
SPT(14)	527641321549992709	0 42 90 114 120 132 154 168 190 202 208 232 280 322	8091360288
SPT(14)	527641333457438237	0 42 50 60 66 102 116 126 140 176 182 192 200 242	19998805816
SPT(14)	527641349375407769	0 14 24 50 60 78 104 138 164 182 192 218 228 242	35916775348
TPT(12)	527641388972874731	0 2 90 92 126 128 198 200 258 260 300 302	75514242310
SPT(14)	527641416332688253	0 24 36 78 100 136 154 180 198 234 256 298 310 334	102874055832