Prime p₀= 1235368086129085367 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: Cruncher Pete
db: batch=77, k=10, 2 28 2 10 2

SPT(16)	1235366666569619851	0 28 42 88 106 168 178 246 262 330 340 402 420 466 480 508	-1419559465516
SPT(16)	1235366982393337363	0 10 30 94 96 100 198 226 258 286 384 388 390 454 474 484	-1103735748004
SPT(16)	1235367351396415423	0 54 60 84 118 130 160 208 300 348 378 390 424 448 454 508	-734732669944
SPT(16)	1235367390999097289	0 48 50 62 114 150 230 234 278 282 362 398 450 462 464 512	-695129988078
STPT(10)	1235367518988879641	0 2 30 32 78 80 126 128 156 158	-567140205726
SPT(16)	1235368064602467041	0 8 12 26 32 36 38 42 176 180 182 186 192 206 210 218	-21526618326
STPT(10)	1235368370559848981	0 2 30 32 78 80 126 128 156 158	284430763614
STPT(10)	1235368791217826537	0 2 30 32 42 44 54 56 84 86	705088741170
STPT(10)	1235368847257300079	0 2 42 44 60 62 78 80 120 122	761128214712
SPT(16)	1235368922663243689	0 10 28 72 88 112 142 154 258 270 300 324 340 384 402 412	836534158322
STPT(10)	1235369224879093301	0 2 6 8 48 50 90 92 96 98	1138750007934