Prime p₀= 513427847430048557 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 22 2 16 2 10 2 28 2 28 2 (?)
a_n: 0 2 24 26 42 44 54 56 84 86 114 116
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: 116
Found by: nenym
db: batch=71, k=12, 22 16 10 28 28

SPT(14)	513427755672570979	0 10 18 22 28 64 108 214 258 294 300 304 312 322	-91757477578
SPT(14)	513427794345819383	0 60 78 114 156 164 186 188 210 218 260 296 314 374	-53084229174
SPT(14)	513427808274674071	0 16 18 72 76 78 172 186 280 282 286 340 342 358	-39155374486
SPT(14)	513427811865433529	0 32 42 44 60 72 84 140 152 164 180 182 192 224	-35564615028
SPT(16)	513427816792753279	0 4 40 72 82 102 112 124 228 240 250 270 280 312 348 352	-30637295278
TPT(12)	513427825345359317	0 2 72 74 120 122 150 152 204 206 222 224	-22084689240
SPT(14)	513427866138510959	0 38 42 108 132 150 180 242 272 290 314 380 384 422	18708462402
SPT(14)	513427878899374913	0 24 48 78 84 126 138 146 158 200 206 236 260 284	31469326356
SPT(14)	513427888289329249	0 12 18 40 88 132 148 192 208 252 300 322 328 340	40859280692
SPT(14)	513427889072110097	0 54 86 92 116 164 192 254 282 330 354 360 392 446	41642061540
SPT(14)	513427897006769839	0 22 70 72 100 112 120 154 162 174 202 204 252 274	49576721282