Prime p₀= 2397283486361766647 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 16 2 22 2 16 2 10 2 (?)
a_n: 0 2 12 14 30 32 54 56 72 74 84 86
All 12 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: [SG-2W]Kurzer
db: batch=81, k=12, 2 10 2 16 2 22

STPT(10)	2397282226558096781	0 2 78 80 138 140 198 200 276 278	-1259803669866
STPT(10)	2397282303931589231	0 2 66 68 108 110 150 152 216 218	-1182430177416
SPT(16)	2397282496245549947	0 12 30 66 74 102 152 156 320 324 374 402 410 446 464 476	-990116216700
SPT(16)	2397282527841444589	0 10 12 22 40 54 108 112 120 124 178 192 210 220 222 232	-958520322058
SPT(16)	2397282826262384149	0 84 130 144 150 178 204 250 258 304 330 358 364 378 424 508	-660099382498
SPT(16)	2397283220779925083	0 4 48 60 78 90 114 130 228 244 268 280 298 310 354 358	-265581841564
SPT(16)	2397283797888642721	0 10 28 42 58 60 78 100 198 220 238 240 256 270 288 298	311526876074
TPT(14)	2397283797978326867	0 2 42 44 84 86 150 152 210 212 282 284 294 296	311616560220
SPT(16)	2397283823796069119	0 14 18 38 44 120 164 168 200 204 248 324 330 350 354 368	337434302472
STPT(10)	2397283830893457851	0 2 36 38 78 80 120 122 156 158	344531691204
SPT(16)	2397283881522908407	0 12 24 94 102 112 120 186 190 256 264 274 282 352 364 376	395161141760