Prime p₀= 4276878030088133537 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: Autofuzzy
db: batch=85, k=10, 2 10 2 28 2

TPT(14)	4276877365741624871	0 2 36 38 138 140 210 212 216 218 300 302 348 350	-664346508666
SPT(16)	4276877374402688309	0 20 38 60 144 150 224 258 260 294 368 374 458 480 498 518	-655685445228
SPT(16)	4276877630911980959	0 2 8 12 44 50 90 132 140 182 222 228 260 264 270 272	-399176152578
SPT(16)	4276877657202024827	0 12 42 54 96 110 120 140 156 176 186 200 242 254 284 296	-372886108710
SPT(16)	4276877742432642637	0 12 52 66 70 96 120 156 286 322 346 372 376 390 430 442	-287655490900
STPT(10)	4276877937461739227	0 2 72 74 102 104 132 134 204 206	-92626394310
SPT(16)	4276878060288902423	0 38 50 84 90 116 120 134 150 164 168 194 200 234 246 284	30200768886
STPT(10)	4276878170196198779	0 2 18 20 60 62 102 104 120 122	140108065242
SPT(16)	4276879506693726131	0 12 66 122 140 180 210 222 290 302 332 372 390 446 500 512	1476605592594
SPT(16)	4276879570165824443	0 24 38 54 56 78 90 126 188 224 236 258 260 276 290 314	1540077690906
SPT(16)	4276879961362955021	0 8 38 60 62 102 116 132 176 192 206 246 248 270 300 308	1931274821484