Prime p₀= 112394076626021261 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 28 2 34 2 52 2 76 2 40 2 (?)
a_n: 0 2 30 32 66 68 120 122 198 200 240 242
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: 242
Found by: emoga
db: batch=67, k=12, 28 34 52 76 40

SPT(14)	112394021784761117	0 24 56 60 84 150 170 186 206 272 296 300 332 356	-54841260144
SPT(14)	112394052282344369	0 8 62 78 108 164 182 210 228 284 314 330 384 392	-24343676892
TPT(12)	112394055657623669	0 2 12 14 180 182 252 254 282 284 348 350	-20968397592
SPT(16)	112394058731236657	0 4 12 40 72 82 90 114 130 154 162 172 204 232 240 244	-17894784604
SPT(14)	112394069354571341	0 8 50 86 96 126 138 140 152 182 192 228 270 278	-7271449920
TPT(12)	112394075429966987	0 2 54 56 60 62 72 74 114 116 150 152	-1196054274
SPT(14)	112394078366864627	0 12 14 20 26 54 62 84 92 120 126 132 134 146	1740843366
SPT(14)	112394085330685331	0 8 12 42 50 62 90 110 138 150 158 188 192 200	8704664070
TPT(12)	112394121438257291	0 2 6 8 78 80 96 98 138 140 150 152	44812236030
SPT(14)	112394123594565403	0 6 24 34 40 54 70 90 106 120 126 136 154 160	46968544142
SPT(14)	112394129157969487	0 6 10 34 66 76 90 100 114 124 156 180 184 190	52531948226