Prime p₀= 2566807567543167857 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: JonS
db: batch=82, k=10, 2 28 2 10 2

SPT(16)	2566804599088827133	0 4 10 24 78 114 130 138 280 288 304 340 394 408 414 418	-2968454340724
SPT(16)	2566804728492824689	0 18 34 52 64 70 90 102 160 172 192 198 210 228 244 262	-2839050343168
STPT(10)	2566804770314784029	0 2 18 20 30 32 42 44 60 62	-2797228383828
SPT(16)	2566806516168494843	0 8 18 48 66 104 126 138 146 158 180 218 236 266 276 284	-1051374673014
SPT(18)	2566807031195331923	0 20 38 48 84 138 146 194 234 260 300 348 356 410 446 456 474 494	-536347835934
SPT(16)	2566807339821748591	0 36 40 46 58 60 88 102 106 120 148 150 162 168 172 208	-227721419266
STPT(10)	2566808123374299377	0 2 42 44 72 74 102 104 144 146	555831131520
SPT(16)	2566808243586854041	0 40 132 180 208 222 228 256 372 400 406 420 448 496 588 628	676043686184
SPT(16)	2566808337702048437	0 84 90 104 114 140 170 260 294 384 414 440 450 464 470 554	770158880580
SPT(16)	2566808399024754779	0 14 42 48 90 104 168 192 230 254 318 332 374 380 408 422	831481586922
STPT(10)	2566808941235869877	0 2 30 32 42 44 54 56 84 86	1373692702020