Prime p₀= 129504672865966589 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 40 2 28 2 16 2 178 2 40 2 (?)
a_n: 0 2 42 44 72 74 90 92 270 272 312 314
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: 314
Found by: Paul
db: batch=67, k=12, 40 28 16 178 40

TPT(12)	129504593043958577	0 2 90 92 132 134 174 176 210 212 222 224	-79822008012
TPT(12)	129504635327762729	0 2 12 14 138 140 150 152 222 224 312 314	-37538203860
TPT(12)	129504645357292937	0 2 12 14 30 32 90 92 114 116 144 146	-27508673652
TPT(12)	129504646499374829	0 2 18 20 72 74 102 104 198 200 222 224	-26366591760
TPT(12)	129504654880871129	0 2 12 14 30 32 72 74 138 140 168 170	-17985095460
SPT(14)	129504658078898077	0 6 34 70 76 162 222 274 334 420 426 462 490 496	-14787068512
SPT(14)	129504682301185523	0 14 36 50 80 96 104 126 134 150 180 194 216 230	9435218934
SPT(16)	129504695585922793	0 6 36 76 78 90 156 184 300 328 394 406 408 448 478 484	22719956204
SPT(14)	129504710298642517	0 16 72 82 130 166 172 180 186 222 270 280 336 352	37432675928
TPT(12)	129504715897718429	0 2 48 50 90 92 102 104 132 134 162 164	43031751840
SPT(14)	129504770062279267	0 6 12 22 34 40 82 84 126 132 144 154 160 166	97196312678