Prime p₀= 562506028709716877 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 40 2 16 2 22 2 4 2 28 2 (?)
a_n: 0 2 42 44 60 62 84 86 90 92 120 122
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: nenym
db: batch=71, k=12, 40 16 22 4 28

SPT(14)	562505981613898799	0 14 78 114 162 182 248 294 360 380 428 464 528 542	-47095818078
TPT(12)	562505986337160377	0 2 54 56 120 122 150 152 204 206 222 224	-42372556500
SPT(14)	562505986478765089	0 24 28 34 40 60 78 94 112 132 138 144 148 172	-42230951788
SPT(14)	562505993085644539	0 10 12 22 28 72 78 142 148 192 198 208 210 220	-35624072338
SPT(14)	562506018361400713	0 28 48 66 70 88 120 136 168 186 190 208 228 256	-10348316164
SPT(14)	562506026451706111	0 52 78 82 106 112 132 196 216 222 246 250 276 328	-2258010766
SPT(16)	562506043749147829	0 52 70 114 118 132 148 174 178 204 220 234 238 282 300 352	15039430952
SPT(14)	562506061705336069	0 10 24 70 90 94 124 168 198 202 222 268 282 292	32995619192
SPT(14)	562506067826373263	0 36 80 84 90 158 186 308 336 404 410 414 458 494	39116656386
SPT(14)	562506071019465887	0 2 26 32 72 132 146 150 164 224 264 270 294 296	42309749010
SPT(14)	562506072669677519	0 78 108 120 168 260 290 312 342 434 482 494 524 602	43959960642