Prime p₀= 276856314623592959 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 10 2 118 2 124 2 82 2 76 2 (?)
a_n: 0 2 12 14 132 134 258 260 342 344 420 422
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: 422
Found by: scrap
db: batch=69, k=12, 10 118 124 82 76

SPT(14)	276856225305963053	0 24 44 66 114 144 150 164 170 200 248 270 290 314	-89317629906
STPT(10)	276856225843205189	0 2 18 20 30 32 42 44 60 62	-88780387770
SPT(14)	276856242812931959	0 8 80 128 140 168 188 354 374 402 414 462 534 542	-71810661000
SPT(14)	276856260719023547	0 2 66 72 116 150 156 176 182 216 260 266 330 332	-53904569412
SPT(14)	276856266797615101	0 18 42 72 88 126 130 168 172 210 226 256 280 298	-47825977858
SPT(14)	276856298412053329	0 58 100 112 114 124 142 180 198 208 210 222 264 322	-16211539630
TPT(12)	276856328785453787	0 2 54 56 192 194 210 212 240 242 264 266	14161860828
TPT(12)	276856334304610349	0 2 18 20 42 44 48 50 78 80 168 170	19681017390
SPT(14)	276856346210897267	0 14 42 84 86 110 114 122 126 150 152 194 222 236	31587304308
SPT(14)	276856358659700641	0 22 52 82 100 162 196 276 310 372 390 420 450 472	44036107682
SPT(14)	276856364827865483	0 86 108 150 156 254 276 278 300 398 404 446 468 554	50204272524