Prime p₀= 1267852912632627857 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 28 2 10 2 10 2 28 2 (?)
a_n: 0 2 30 32 42 44 54 56 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: Megacruncher
db: batch=77, k=10, 2 28 2 10 2

SPT(16)	1267850850945076553	0 30 44 56 60 78 80 116 168 204 206 224 228 240 254 284	-2061687551304
SPT(16)	1267851601873198591	0 6 16 106 112 132 142 190 222 270 280 300 306 396 406 412	-1310759429266
SPT(16)	1267852221046574213	0 30 50 66 84 86 156 164 240 248 318 320 338 354 374 404	-691586053644
SPT(16)	1267852448988453319	0 10 24 34 52 60 90 172 192 274 304 312 330 340 354 364	-463644174538
STPT(10)	1267852547385530549	0 2 18 20 60 62 102 104 120 122	-365247097308
STPT(10)	1267852597274660669	0 2 18 20 30 32 42 44 60 62	-315357967188
TPT(14)	1267853016118856621	0 2 18 20 60 62 108 110 126 128 156 158 198 200	103486228764
TPT(14)	1267853209195723877	0 2 24 26 150 152 210 212 264 266 270 272 282 284	296563096020
STPT(10)	1267853343637379669	0 2 78 80 120 122 162 164 240 242	431004751812
SPT(16)	1267853744919128119	0 34 42 58 78 82 124 142 180 198 240 244 264 280 288 322	832286500262
SPT(16)	1267853779374911297	0 2 24 30 62 74 132 150 164 182 240 252 284 290 312 314	866742283440