Prime p₀= 82874609189579321 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 88 2 76 2 16 2 40 2 40 2 (?)
a_n: 0 2 90 92 168 170 186 188 228 230 270 272
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: 272
Found by: emoga
db: batch=67, k=12, 88 76 16 40 40

TPT(12)	82874569503076397	0 2 54 56 90 92 102 104 132 134 144 146	-39686502924
SPT(14)	82874585546851837	0 6 40 70 72 82 100 186 204 214 216 246 280 286	-23642727484
SPT(14)	82874587194955921	0 18 52 70 72 82 88 120 126 136 138 156 190 208	-21994623400
SPT(14)	82874589927608023	0 96 108 138 150 168 186 208 226 244 256 286 298 394	-19261971298
TPT(12)	82874592970292897	0 2 42 44 54 56 114 116 144 146 300 302	-16219286424
SPT(14)	82874607568422821	0 2 6 50 60 72 78 110 116 128 138 182 186 188	-1621156500
TPT(12)	82874619317293379	0 2 78 80 102 104 132 134 168 170 252 254	10127714058
SPT(14)	82874623114568633	0 36 50 54 56 98 110 174 186 228 230 234 248 284	13924989312
SPT(14)	82874626761821117	0 14 42 44 80 84 114 122 152 156 192 194 222 236	17572241796
SPT(14)	82874639018036609	0 2 18 32 38 42 90 410 458 462 468 482 498 500	29828457288
SPT(14)	82874648766461921	0 6 20 36 48 56 90 98 132 140 152 168 182 188	39576882600