Prime p₀= 1292617591615845767 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 22 2 16 2 16 2 22 2 (?)
a_n: 0 2 24 26 42 44 60 62 84 86
All 10 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 86
Found by: Dirk Broer
db: batch=77, k=10, 2 22 2 16 2

STPT(12)	1292616413194534457	0 2 12 14 30 32 54 56 72 74 84 86	-1178421311310
SPT(16)	1292616519886384961	0 36 38 42 50 56 66 80 168 182 192 198 206 210 212 248	-1071729460806
SPT(16)	1292616537031059907	0 16 120 160 162 172 186 232 324 370 384 394 396 436 540 556	-1054584785860
TPT(14)	1292616885273889709	0 2 30 32 42 44 198 200 240 242 312 314 330 332	-706341956058
SPT(16)	1292616900388331059	0 22 24 48 64 78 112 132 280 300 334 348 364 388 390 412	-691227514708
TPT(14)	1292616943609144157	0 2 12 14 54 56 114 116 144 146 210 212 240 242	-648006701610
SPT(20)	1292617809934367317	0 4 34 52 66 90 100 102 112 126 220 234 244 246 256 280 294 312 342 346	218318521550
STPT(10)	1292617903705715267	0 2 90 92 102 104 114 116 204 206	312089869500
SPT(16)	1292618384319942061	0 16 40 48 76 78 88 106 180 198 208 210 238 246 270 286	792704096294
SPT(16)	1292618715920446051	0 30 40 46 60 70 106 148 180 222 258 268 282 288 298 328	1124304600284
SPT(16)	1292618862802830313	0 4 24 58 66 78 88 136 168 216 226 238 246 280 300 304	1271186984546