Prime p₀= 2327708163025619741 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 76 2 40 2 46 2 40 2 76 2 (?)
a_n: 0 2 78 80 120 122 168 170 210 212 288 290
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: 290
Found by: Landjunge
db: batch=81, k=12, 2 76 2 40 2 46

SPT(16)	2327707049376147169	0 42 48 70 78 90 108 132 178 202 220 232 240 262 268 310	-1113649472572
TPT(14)	2327707558587701489	0 2 42 44 78 80 132 134 138 140 168 170 180 182	-604437918252
SPT(16)	2327707595497842247	0 82 112 180 184 186 214 232 264 282 310 312 316 384 414 496	-567527777494
TPT(14)	2327707735813664717	0 2 60 62 84 86 132 134 144 146 210 212 294 296	-427211955024
SPT(16)	2327707847196986953	0 4 6 40 58 138 160 180 244 264 286 366 384 418 420 424	-315828632788
SPT(16)	2327708137468558643	0 18 24 36 50 74 78 86 198 206 210 234 248 260 266 284	-25557061098
SPT(16)	2327708518070549891	0 8 26 96 120 146 156 168 188 200 210 236 260 330 348 356	355044930150
SPT(16)	2327708539082677603	0 40 46 48 58 114 118 160 264 306 310 366 376 378 384 424	376057057862
SPT(16)	2327708713881595271	0 6 132 182 230 236 266 318 320 372 402 408 456 506 632 638	550855975530
SPT(16)	2327708715264555551	0 90 102 122 152 162 186 192 260 266 290 300 330 350 362 452	552238935810
STPT(10)	2327708717497851971	0 2 6 8 48 50 90 92 96 98	554472232230