Prime p₀= 115349766519193937 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 22 2 28 2 28 2 4 2 40 2 (?)
a_n: 0 2 24 26 54 56 84 86 90 92 132 134
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: 134
Found by: emoga
db: batch=67, k=12, 22 28 28 4 40

TPT(12)	115349687743586039	0 2 42 44 78 80 102 104 120 122 228 230	-78775607898
SPT(14)	115349697661039339	0 28 54 64 70 108 112 150 154 192 198 208 234 262	-68858154598
SPT(14)	115349712633180833	0 30 38 44 56 90 120 134 164 198 210 216 224 254	-53886013104
SPT(14)	115349716876403407	0 34 46 72 84 90 124 132 166 172 184 210 222 256	-49642790530
TPT(12)	115349724952458497	0 2 12 14 54 56 72 74 114 116 354 356	-41566735440
SPT(14)	115349751340011179	0 14 24 32 60 62 102 122 162 164 192 200 210 224	-15179182758
SPT(14)	115349779518026351	0 6 20 26 62 68 72 86 90 96 132 138 152 158	12998832414
SPT(14)	115349781428365111	0 6 42 60 160 172 192 196 216 228 328 346 382 388	14909171174
TPT(12)	115349781554951561	0 2 48 50 60 62 126 128 198 200 210 212	15035757624
TPT(12)	115349785817474321	0 2 78 80 126 128 168 170 180 182 198 200	19298280384
STPT(10)	115349802956494859	0 2 18 20 30 32 42 44 60 62	36437300922