Prime p₀= 1231734080302312421 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 46 2 118 2 118 2 46 2 (?)
a_n: 0 2 48 50 168 170 288 290 336 338
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: 338
Found by: Megacruncher
db: batch=77, k=10, 2 46 2 118 2

SPT(16)	1231731857116349759	0 48 60 74 140 144 224 258 260 294 374 378 444 458 470 518	-2223185962662
SPT(16)	1231732021777082933	0 6 18 20 78 120 126 176 258 308 314 356 414 416 428 434	-2058525229488
SPT(16)	1231732184670266347	0 22 46 76 90 144 154 186 190 222 232 286 300 330 354 376	-1895632046074
STPT(10)	1231732232935556249	0 2 18 20 30 32 42 44 60 62	-1847366756172
SPT(16)	1231732979298999577	0 12 24 36 52 54 100 136 210 246 292 294 310 322 334 346	-1101003312844
SPT(16)	1231733302791727741	0 12 66 76 82 90 136 150 178 192 238 246 252 262 316 328	-777510584680
SPT(16)	1231734273472377769	0 12 28 42 70 112 120 208 222 310 318 360 388 402 418 430	193170065348
STPT(10)	1231734283626169187	0 2 12 14 72 74 132 134 144 146	203323856766
SPT(16)	1231734377549120813	0 18 36 54 60 78 84 120 134 170 176 194 200 218 236 254	297246808392
TPT(14)	1231734433821911429	0 2 12 14 18 20 132 134 180 182 198 200 282 284	353519599008
SPT(16)	1231734814804710407	0 42 50 92 140 144 164 182 234 252 272 276 324 366 374 416	734502397986