Prime p₀= 377764837792689689 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 58 2 40 2 4 2 112 2 16 2 (?)
a_n: 0 2 60 62 102 104 108 110 222 224 240 242
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: Cruncher Pete
db: batch=70, k=12, 58 40 4 112 16

SPT(14)	377764762687098859	0 28 108 112 168 174 198 274 298 304 360 364 444 472	-75105590830
SPT(14)	377764771791772501	0 16 36 42 58 70 132 136 198 210 226 232 252 268	-66000917188
TPT(12)	377764774704181301	0 2 138 140 216 218 288 290 390 392 468 470	-63088508388
SPT(14)	377764789374170371	0 10 40 60 66 90 96 166 172 196 202 222 252 262	-48418519318
SPT(14)	377764794891751307	0 50 60 66 102 104 126 140 162 164 200 206 216 266	-42900938382
SPT(14)	377764820290766599	0 12 22 28 40 42 108 304 370 372 384 390 400 412	-17501923090
SPT(14)	377764850227005077	0 2 30 44 50 62 92 132 162 174 180 194 222 224	12434315388
SPT(16)	377764850689160497	0 6 40 52 76 112 154 156 220 222 264 300 324 336 370 376	12896470808
SPT(14)	377764858975395149	0 12 14 42 48 74 102 140 168 194 200 228 230 242	21182705460
SPT(14)	377764867953809779	0 24 42 58 60 72 78 94 100 112 114 130 148 172	30161120090
SPT(14)	377764942181638589	0 14 42 62 102 140 152 162 174 212 252 272 300 314	104388948900