Prime p₀= 1267307936929732697 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: Megacruncher
db: batch=77, k=10, 2 22 2 16 2

SPT(16)	1267306451222726269	0 54 88 90 94 102 108 130 132 154 160 168 172 174 208 262	-1485707006428
STPT(10)	1267306465734622109	0 2 18 20 30 32 42 44 60 62	-1471195110588
STPT(10)	1267306763386309727	0 2 42 44 72 74 102 104 144 146	-1173543422970
TPT(14)	1267306900019547899	0 2 108 110 180 182 210 212 360 362 378 380 462 464	-1036910184798
SPT(16)	1267307011963476329	0 32 42 60 62 84 98 104 108 114 128 150 152 170 180 212	-924966256368
TPT(14)	1267307173979102279	0 2 60 62 78 80 282 284 312 314 372 374 420 422	-762950630418
TPT(14)	1267307979052376291	0 2 30 32 120 122 156 158 186 188 258 260 288 290	42122643594
SPT(16)	1267308032558166437	0 12 20 42 80 102 114 144 152 182 194 216 254 276 284 296	95628433740
STPT(10)	1267308148496769287	0 2 30 32 42 44 54 56 84 86	211567036590
STPT(10)	1267308228017083919	0 2 18 20 30 32 42 44 60 62	291087351222
SPT(16)	1267308358542994949	0 20 38 42 80 90 150 174 188 212 272 282 320 324 342 362	421613262252