Prime p₀= 7315223927103809 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 10 2 64 2 82 2 4 2 40 2 (?)
a_n: 0 2 12 14 78 80 162 164 168 170 210 212
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: 212
Found by: crashtech
db: batch=62, k=12, 10 64 82 4 40

SPT(16)	7315183047184511	0 32 36 50 56 78 92 102 116 126 140 162 168 182 186 218	-40879919298
SPT(14)	7315188943805167	0 12 34 42 46 60 94 162 196 210 214 222 244 256	-34983298642
SPT(14)	7315205672724739	0 18 48 60 72 84 88 114 118 130 142 154 184 202	-18254379070
SPT(14)	7315207932556397	0 2 30 42 60 84 110 174 200 224 242 254 282 284	-15994547412
SPT(14)	7315214429038441	0 102 112 120 142 160 168 220 228 246 268 276 286 388	-9498065368
SPT(14)	7315221054307367	0 26 36 42 50 56 116 120 180 186 194 200 210 236	-2872796442
TPT(12)	7315224736618661	0 2 18 20 78 80 90 92 126 128 168 170	809514852
SPT(14)	7315229949335431	0 12 58 70 76 90 96 142 148 162 168 180 226 238	6022231622
SPT(20)	7315240127395477	0 6 16 40 70 72 76 96 102 106 180 184 190 210 214 216 246 270 280 286	16200291668
TPT(12)	7315240282886441	0 2 48 50 78 80 90 92 138 140 168 170	16355782632
STPT(10)	7315241171882489	0 2 18 20 30 32 42 44 60 62	17244778680