Prime p₀= 425582284293944801 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 76 2 10 2 34 2 28 2 10 2 (?)
a_n: 0 2 78 80 90 92 126 128 156 158 168 170
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: Cruncher Pete
db: batch=70, k=12, 76 10 34 28 10

SPT(14)	425582156932017457	0 30 42 52 60 72 94 102 124 136 144 154 166 196	-127361927344
SPT(14)	425582194144329347	0 2 24 30 32 86 116 180 210 264 266 272 294 296	-90149615454
SPT(14)	425582245214933119	0 4 70 82 102 130 132 172 174 202 222 234 300 304	-39079011682
SPT(14)	425582250312305509	0 10 64 70 78 108 120 142 154 184 192 198 252 262	-33981639292
SPT(14)	425582258880679273	0 6 18 24 64 66 70 84 88 90 130 136 148 154	-25413265528
SPT(14)	425582276205854267	0 14 24 66 80 86 104 156 174 180 194 236 246 260	-8088090534
SPT(16)	425582295724669729	0 22 42 88 90 100 112 130 132 150 162 172 174 220 240 262	11430724928
SPT(16)	425582297117592101	0 12 26 42 48 68 90 152 156 218 240 260 266 282 296 308	12823647300
TPT(12)	425582309885331827	0 2 60 62 90 92 114 116 294 296 384 386	25591387026
SPT(14)	425582314983121687	0 6 46 52 136 150 202 270 322 336 420 426 466 472	30689176886
STPT(10)	425582332862682179	0 2 18 20 30 32 42 44 60 62	48568737378