Prime p₀= 2301690426641360633 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 104 12 10 8 4 126 6 74 6 126 4 8 10 12 104 (?)
a_n: 0 104 116 126 134 138 264 270 344 350 476 480 488 498 510 614
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: 614
Found by: FritzB
db: batch=81, k=16, 104 12 10 8 4 126 6 74

SPT(16)	2301689365021684549	0 18 22 42 72 84 88 112 150 174 178 190 220 240 244 262	-1061619676084
STPT(10)	2301689377644573347	0 2 12 14 72 74 132 134 144 146	-1048996787286
SPT(18)	2301689423676326741	0 36 38 78 80 140 156 176 182 186 192 212 228 288 290 330 332 368	-1002965033892
STPT(10)	2301689830867012679	0 2 42 44 60 62 78 80 120 122	-595774347954
SPT(16)	2301689893715542769	0 8 24 62 74 90 92 104 138 150 152 168 180 218 234 242	-532925817864
SPT(16)	2301690385102772747	0 44 56 74 122 144 150 174 182 206 212 234 282 300 312 356	-41538587886
STPT(10)	2301690486843352901	0 2 6 8 18 20 30 32 36 38	60201992268
STPT(10)	2301690751731814841	0 2 156 158 168 170 180 182 336 338	325090454208
SPT(16)	2301691346822559707	0 32 44 54 92 114 140 144 152 156 182 204 242 252 264 296	920181199074
SPT(16)	2301691535610274499	0 30 32 38 54 90 194 200 222 228 332 368 384 390 392 422	1108968913866
SPT(16)	2301691557827651963	0 18 36 50 140 158 168 206 240 278 288 306 396 410 428 446	1131186291330