Prime p₀= 1267877636958517729 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 34 50 48 30 12 36 4 14 4 36 12 30 48 50 34 (?)
a_n: 0 34 84 132 162 174 210 214 228 232 268 280 310 358 408 442
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: 442
Found by: Megacruncher
db: batch=77, k=16, 34 50 48 30 12 36 4 14

SPT(16)	1267876056871690727	0 26 54 114 116 222 240 266 270 296 314 420 422 482 510 536	-1580086827002
SPT(16)	1267876369657117133	0 8 44 50 90 128 146 156 188 198 216 254 294 300 336 344	-1267301400596
STPT(10)	1267876520968647377	0 2 12 14 72 74 132 134 144 146	-1115989870352
SPT(16)	1267877049694918807	0 4 6 22 36 42 72 102 184 214 244 250 264 280 282 286	-587263598922
STPT(10)	1267877277590363507	0 2 60 62 72 74 84 86 144 146	-359368154222
STPT(10)	1267877305500003311	0 2 36 38 78 80 120 122 156 158	-331458514418
TPT(14)	1267878226742234489	0 2 18 20 42 44 72 74 228 230 258 260 312 314	589783716760
SPT(16)	1267878371871513001	0 6 22 36 70 88 90 136 162 208 210 228 262 276 292 298	734912995272
STPT(10)	1267878483897540881	0 2 36 38 78 80 120 122 156 158	846939023152
SPT(16)	1267878515469626861	0 26 66 126 152 192 198 210 218 230 236 276 302 362 402 428	878511109132
SPT(18)	1267879268752276721	0 6 32 48 120 162 168 176 216 242 282 290 296 338 410 426 452 458	1631793758992