Prime p₀= 456496616380874651 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 28 2 64 2 28 2 40 2 10 2 (?)
a_n: 0 2 30 32 96 98 126 128 168 170 180 182
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: 182
Found by: Cruncher Pete
db: batch=70, k=12, 28 64 28 40 10

TPT(12)	456496539957484769	0 2 72 74 78 80 162 164 252 254 318 320	-76423389882
SPT(14)	456496558087586689	0 54 60 70 114 138 148 204 214 238 282 292 298 352	-58293287962
SPT(14)	456496563673290379	0 24 40 42 52 54 70 192 208 210 220 222 238 262	-52707584272
SPT(14)	456496578599266357	0 6 22 34 52 76 94 102 120 144 162 174 190 196	-37781608294
SPT(14)	456496580784141641	0 30 32 60 72 90 150 182 242 260 272 300 302 332	-35596733010
SPT(14)	456496607075145281	0 50 56 80 98 102 108 110 116 120 138 162 168 218	-9305729370
TPT(12)	456496628836662497	0 2 54 56 114 116 144 146 222 224 282 284	12455787846
SPT(14)	456496649190801721	0 6 10 12 28 76 88 90 102 150 166 168 172 178	32809927070
SPT(14)	456496665381086497	0 12 24 40 52 60 112 192 244 252 264 280 292 304	49000211846
SPT(14)	456496674533757617	0 6 62 102 110 114 152 174 212 216 224 264 320 326	58152882966
SPT(14)	456496693945798267	0 4 10 40 46 114 126 154 166 234 240 270 276 280	77564923616