Prime p₀= 268234340873316281 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 4 2 28 2 22 2 28 2 28 2 (?)
a_n: 0 2 6 8 36 38 60 62 90 92 120 122
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: 122
Found by: desktop64
db: batch=69, k=12, 4 28 22 28 28

SPT(14)	268234286843065493	0 20 38 60 104 114 140 198 224 234 278 300 318 338	-54030250788
SPT(14)	268234294821390203	0 20 26 38 60 104 108 176 180 224 246 258 264 284	-46051926078
TPT(12)	268234303213307867	0 2 72 74 120 122 252 254 270 272 294 296	-37660008414
TPT(12)	268234306062974267	0 2 30 32 84 86 90 92 102 104 120 122	-34810342014
TPT(12)	268234329781908911	0 2 120 122 126 128 150 152 168 170 198 200	-11091407370
SPT(14)	268234336328992667	0 14 32 36 62 96 104 132 140 174 200 204 222 236	-4544323614
TPT(14)	268234367325214217	0 2 42 44 54 56 72 74 90 92 102 104 144 146	26451897936
STPT(14)	268234367325214217	0 2 42 44 54 56 72 74 90 92 102 104 144 146	26451897936
SPT(14)	268234367325214217	0 2 42 44 54 56 72 74 90 92 102 104 144 146	26451897936
SPT(14)	268234375259572067	0 14 20 30 42 84 86 150 152 194 206 216 222 236	34386255786
SPT(14)	268234376186876551	0 6 28 46 78 90 126 190 226 238 270 288 310 316	35313560270