Prime p₀= 576565393479136769 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 28 2 76 2 28 2 22 2 4 2 (?)
a_n: 0 2 30 32 108 110 138 140 162 164 168 170
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: 170
Found by: ladmo
db: batch=71, k=12, 28 76 28 22 4

SPT(14)	576565328166024347	0 42 86 120 126 132 150 152 170 176 182 216 260 302	-65313112422
SPT(16)	576565336898867159	0 8 42 78 104 138 158 162 200 204 224 258 284 320 354 362	-56580269610
SPT(16)	576565340006472833	0 56 66 78 80 108 120 126 128 134 146 174 176 188 198 254	-53472663936
STPT(10)	576565371952493981	0 2 36 38 78 80 120 122 156 158	-21526642788
SPT(14)	576565377175749659	0 14 42 54 74 110 194 210 294 330 350 362 390 404	-16303387110
SPT(14)	576565386407784247	0 24 34 42 52 60 96 160 196 204 214 222 232 256	-7071352522
TPT(12)	576565398124391189	0 2 42 44 48 50 120 122 132 134 138 140	4645254420
SPT(14)	576565398128895547	0 10 22 52 64 126 196 270 340 402 414 444 456 466	4649758778
SPT(14)	576565401368492131	0 46 58 82 96 100 102 136 138 142 156 180 192 238	7889355362
SPT(14)	576565415982082727	0 12 26 32 50 74 110 126 162 186 204 210 224 236	22502945958
SPT(14)	576565467854382547	0 10 22 126 136 150 172 234 256 270 280 384 396 406	74375245778