Prime p₀= 259587961657418291 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 58 2 124 2 52 2 58 2 64 2 (?)
a_n: 0 2 60 62 186 188 240 242 300 302 366 368
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: 368
Found by: desktop64
db: batch=69, k=12, 58 124 52 58 64

SPT(14)	259587855146109383	0 14 24 54 126 134 158 186 210 218 290 320 330 344	-106511308908
SPT(16)	259587874419203989	0 18 22 42 64 112 120 138 154 172 180 228 250 270 274 292	-87238214302
SPT(14)	259587893417105171	0 32 48 50 72 80 98 150 168 176 198 200 216 248	-68240313120
SPT(16)	259587896496042511	0 40 82 88 90 130 178 192 196 210 258 298 300 306 348 388	-65161375780
SPT(14)	259587922639447057	0 6 40 60 82 90 154 222 286 294 316 336 370 376	-39017971234
SPT(14)	259587945087019097	0 24 26 66 90 104 174 182 252 266 290 330 332 356	-16570399194
TPT(12)	259587962352415547	0 2 102 104 114 116 222 224 264 266 300 302	694997256
SPT(14)	259587977936798983	0 6 16 30 106 120 124 150 154 168 244 258 268 274	16279380692
SPT(14)	259587984070699153	0 18 64 88 90 100 150 154 204 214 216 240 286 304	22413280862
SPT(14)	259587985715330429	0 14 48 50 72 98 114 188 204 230 252 254 288 302	24057912138
SPT(14)	259587987600145859	0 12 14 30 44 50 92 120 162 168 182 198 200 212	25942727568