Prime p₀= 544464048037028807 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 28 2 40 2 10 2 28 2 4 2 (?)
a_n: 0 2 30 32 72 74 84 86 114 116 120 122
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: 122
Found by: Bryan
db: batch=56, k=12, 28 40 10 28 4

SPT(14)	544463958867036697	0 12 90 112 114 124 126 130 132 142 144 166 244 256	-89169992110
SPT(16)	544463979746289653	0 14 30 68 74 86 98 114 140 156 168 180 186 224 240 254	-68290739154
SPT(14)	544463997193447039	0 10 22 30 88 114 154 228 268 294 352 360 372 382	-50843581768
SPT(14)	544464000513333337	0 24 34 64 82 90 120 154 184 192 210 240 250 274	-47523695470
TPT(12)	544464025320045239	0 2 12 14 48 50 78 80 90 92 138 140	-22716983568
SPT(14)	544464030757449563	0 18 48 90 150 158 216 320 378 386 446 488 518 536	-17279579244
SPT(14)	544464084491973923	0 14 26 50 54 78 90 104 116 140 144 168 180 194	36454945116
SPT(14)	544464093801099113	0 20 36 48 50 56 98 186 228 234 236 248 264 284	45764070306
SPT(14)	544464110285631881	0 30 38 50 66 80 102 146 168 182 198 210 218 248	62248603074
TPT(12)	544464153221597429	0 2 18 20 30 32 42 44 78 80 120 122	105184568622
SPT(14)	544464155559874063	0 24 30 66 70 78 114 160 196 204 208 244 250 274	107522845256