Prime p₀= 456491707412432231 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 64 2 58 2 70 2 76 2 70 2 (?)
a_n: 0 2 66 68 126 128 198 200 276 278 348 350
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: 350
Found by: scrap
db: batch=70, k=12, 64 58 70 76 70

TPT(12)	456491658234219401	0 2 78 80 96 98 180 182 276 278 288 290	-49178212830
SPT(14)	456491673146577569	0 20 30 62 68 74 98 174 198 204 210 242 252 272	-34265854662
TPT(12)	456491674986191357	0 2 60 62 84 86 102 104 132 134 162 164	-32426240874
TPT(12)	456491692792067741	0 2 48 50 186 188 210 212 306 308 438 440	-14620364490
TPT(12)	456491692917721751	0 2 6 8 36 38 66 68 138 140 288 290	-14494710480
SPT(14)	456491701559736659	0 32 68 90 102 110 138 194 222 230 242 264 300 332	-5852695572
SPT(14)	456491712325204783	0 10 24 34 76 90 120 154 184 198 240 250 264 274	4912772552
SPT(14)	456491718488558549	0 12 32 38 44 80 104 108 132 168 174 180 200 212	11076126318
SPT(14)	456491753561739569	0 14 18 38 44 84 90 98 104 144 150 170 174 188	46149307338
TPT(12)	456491756592066119	0 2 12 14 72 74 138 140 150 152 222 224	49179633888
STPT(10)	456491771208853277	0 2 42 44 72 74 102 104 144 146	63796421046