Prime p₀= 456496822061796149 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 58 2 10 2 28 2 64 2 58 2 (?)
a_n: 0 2 60 62 72 74 102 104 168 170 228 230
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: 230
Found by: Cruncher Pete
db: batch=70, k=12, 58 10 28 64 58

SPT(14)	456496674533757617	0 6 62 102 110 114 152 174 212 216 224 264 320 326	-147528038532
SPT(14)	456496693945798267	0 4 10 40 46 114 126 154 166 234 240 270 276 280	-128115997882
TPT(12)	456496733416273799	0 2 12 14 18 20 42 44 132 134 210 212	-88645522350
STPT(10)	456496744146032477	0 2 24 26 42 44 60 62 84 86	-77915763672
TPT(12)	456496809578824277	0 2 84 86 90 92 132 134 240 242 312 314	-12482971872
SPT(14)	456496810588220113	0 28 60 66 78 126 136 138 148 196 208 214 246 274	-11473576036
SPT(14)	456496841801774281	0 6 48 58 82 100 118 120 138 156 180 190 232 238	19739978132
TPT(12)	456496844609486489	0 2 18 20 90 92 180 182 210 212 282 284	22547690340
SPT(14)	456496850559666131	0 20 36 48 56 116 150 176 210 270 278 290 306 326	28497869982
TPT(12)	456496850905142951	0 2 36 38 126 128 138 140 198 200 210 212	28843346802
TPT(12)	456496857770895677	0 2 72 74 150 152 234 236 240 242 420 422	35709099528