Prime p₀= 1267466529583164257 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 10 2 28 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 72 74 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 10 2 28 2

TPT(14)	1267465241408820329	0 2 12 14 30 32 72 74 78 80 108 110 150 152	-1288174343928
STPT(10)	1267465279795769147	0 2 30 32 60 62 90 92 120 122	-1249787395110
SPT(16)	1267465308237772979	0 32 62 90 114 128 132 210 212 290 294 308 332 360 390 422	-1221345391278
STPT(10)	1267465832484901097	0 2 42 44 72 74 102 104 144 146	-697098263160
SPT(16)	1267465931054709017	0 74 86 90 132 134 150 240 386 476 492 494 536 540 552 626	-598528455240
SPT(16)	1267466300293192091	0 42 50 126 158 182 198 236 252 290 306 330 362 438 446 488	-229289972166
STPT(10)	1267466613521679017	0 2 42 44 72 74 102 104 144 146	83938514760
SPT(16)	1267466975312534089	0 10 34 70 88 112 114 120 142 148 150 174 192 228 252 262	445729369832
TPT(14)	1267467237033321617	0 2 54 56 60 62 72 74 192 194 210 212 234 236	707450157360
SPT(16)	1267467333600869227	0 46 66 102 126 186 210 220 246 256 280 340 364 400 420 466	804017704970
STPT(10)	1267467454816205471	0 2 6 8 48 50 90 92 96 98	925233041214