Prime p₀= 2324767930053288749 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 28 2 34 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 78 80 108 110 120 122
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: 122
Found by: Merowig
db: batch=81, k=12, 2 10 2 28 2 34

SPT(16)	2324766061724933471	0 42 50 72 102 116 128 140 198 210 222 236 266 288 296 338	-1868328355278
SPT(16)	2324766069606920803	0 6 34 40 58 100 106 118 156 168 174 216 234 240 268 274	-1860446367946
SPT(16)	2324766507017603057	0 44 50 56 110 122 140 156 230 246 264 276 330 336 342 386	-1423035685692
STPT(10)	2324766710219607089	0 2 18 20 60 62 102 104 120 122	-1219833681660
SPT(16)	2324767241131381621	0 16 18 22 42 60 102 142 156 196 238 256 276 280 282 298	-688921907128
SPT(16)	2324767334473304911	0 22 42 58 66 78 82 88 120 126 130 142 150 166 186 208	-595579983838
SPT(16)	2324768712347555641	0 58 96 100 118 192 198 220 258 280 286 360 378 382 420 478	782294266892
SPT(16)	2324768843127487373	0 14 24 26 44 68 86 96 128 138 156 180 198 200 210 224	913074198624
TPT(14)	2324768951678575667	0 2 114 116 144 146 180 182 192 194 210 212 234 236	1021625286918
STPT(10)	2324769525893600897	0 2 42 44 72 74 102 104 144 146	1595840312148
SPT(16)	2324769842941517893	0 18 36 48 64 76 106 148 186 228 258 270 286 298 316 334	1912888229144