Prime p₀= 509059414327796531 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 64 2 10 2 130 2 76 2 10 2 (?)
a_n: 0 2 66 68 78 80 210 212 288 290 300 302
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: 302
Found by: scrap
db: batch=71, k=12, 64 10 130 76 10

SPT(14)	509059348112674207	0 6 60 66 84 90 114 162 186 192 210 216 270 276	-66215122324
TPT(12)	509059348779319031	0 2 78 80 150 152 156 158 198 200 330 332	-65548477500
SPT(14)	509059350190035457	0 22 60 64 94 120 180 196 256 282 312 316 354 376	-64137761074
SPT(14)	509059358349261121	0 58 90 100 160 166 190 216 240 246 306 316 348 406	-55978535410
SPT(14)	509059381171643881	0 36 76 78 90 102 126 172 196 208 220 222 262 298	-33156152650
SPT(14)	509059387177640071	0 6 28 100 142 178 198 220 240 276 318 390 412 418	-27150156460
SPT(14)	509059420832281667	0 12 20 90 144 174 182 234 242 272 326 396 404 416	6504485136
SPT(14)	509059439958657169	0 40 54 72 82 108 124 138 154 180 190 208 222 262	25630860638
SPT(16)	509059461065037481	0 22 48 70 100 106 120 130 198 208 222 228 258 280 306 328	46737240950
SPT(14)	509059523814028351	0 6 40 126 132 138 150 178 190 196 202 288 322 328	109486231820
TPT(12)	509059525231342439	0 2 48 50 132 134 228 230 252 254 258 260	110903545908