Prime p₀= 1246843748893209767 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: Cruncher Pete
db: batch=77, k=10, 2 22 2 16 2

SPT(16)	1246842979234684697	0 12 110 120 164 176 246 266 270 290 360 372 416 426 524 536	-769658525070
TPT(14)	1246843106427445517	0 2 90 92 144 146 210 212 222 224 312 314 324 326	-642465764250
STPT(10)	1246843132424652941	0 2 6 8 48 50 90 92 96 98	-616468556826
SPT(16)	1246843446326876621	0 6 12 38 56 60 90 116 132 158 188 192 210 236 242 248	-302566333146
SPT(16)	1246843448704067243	0 60 84 138 150 168 198 200 204 206 236 254 266 320 344 404	-300189142524
STPT(10)	1246843702802147501	0 2 6 8 18 20 30 32 36 38	-46091062266
SPT(16)	1246843811117168461	0 10 22 36 40 46 70 82 126 138 162 168 172 186 198 208	62223958694
SPT(16)	1246844006626036129	0 10 12 24 48 54 58 82 210 234 238 244 268 280 282 292	257732826362
STPT(10)	1246844018960198777	0 2 30 32 42 44 54 56 84 86	270066989010
SPT(16)	1246844065121973209	0 8 30 42 48 80 90 114 188 212 222 254 260 272 294 302	316228763442
STPT(10)	1246844113771295927	0 2 24 26 42 44 60 62 84 86	364878086160