Prime p₀= 281251630837170737 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 40 2 28 2 10 2 34 2 10 2 (?)
a_n: 0 2 42 44 72 74 84 86 120 122 132 134
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: desktop64
db: batch=69, k=12, 40 28 10 34 10

STPT(10)	281251578498605129	0 2 18 20 30 32 42 44 60 62	-52338565608
SPT(14)	281251596852267007	0 22 96 124 130 154 184 192 222 246 252 280 354 376	-33984903730
SPT(14)	281251608553685173	0 24 34 48 60 136 178 186 228 304 316 330 340 364	-22283485564
SPT(14)	281251624485838673	0 8 18 24 36 44 80 84 120 128 140 146 156 164	-6351332064
SPT(14)	281251628029109383	0 16 46 48 90 100 120 154 174 184 226 228 258 274	-2808061354
SPT(14)	281251628813547901	0 6 10 60 66 112 130 132 150 196 202 252 256 262	-2023622836
TPT(12)	281251636187113619	0 2 18 20 30 32 60 62 150 152 198 200	5349942882
SPT(14)	281251643831996599	0 4 24 48 90 108 124 138 154 172 214 238 258 262	12994825862
SPT(14)	281251646560283149	0 28 60 70 72 90 100 102 112 130 132 142 174 202	15723112412
SPT(14)	281251652611963729	0 40 108 138 154 174 178 234 238 258 274 304 372 412	21774792992
TPT(12)	281251674972221099	0 2 12 14 42 44 108 110 150 152 282 284	44135050362