Prime p₀= 404014989872496971 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 136 2 70 2 34 2 28 2 10 2 (?)
a_n: 0 2 138 140 210 212 246 248 276 278 288 290
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: 290
Found by: Cruncher Pete
db: batch=70, k=12, 136 70 34 28 10

SPT(14)	404014898551998649	0 4 54 70 88 94 108 154 168 174 192 208 258 262	-91320498322
SPT(14)	404014900011267803	0 18 30 60 86 98 140 144 186 198 224 254 266 284	-89861229168
TPT(12)	404014907395822949	0 2 90 92 120 122 270 272 282 284 330 332	-82476674022
SPT(14)	404014942482342053	0 14 30 44 48 80 84 170 174 206 210 224 240 254	-47390154918
SPT(14)	404014950600007907	0 32 62 72 86 90 132 140 182 186 200 210 240 272	-39272489064
SPT(14)	404014970895578533	0 18 40 78 88 148 150 208 210 270 280 318 340 358	-18976918438
SPT(14)	404015004244699543	0 54 70 78 124 148 154 300 306 330 376 384 400 454	14372202572
SPT(14)	404015039189963651	0 20 38 42 62 72 80 90 98 108 128 132 150 170	49317466680
SPT(14)	404015057064043487	0 30 54 60 66 74 80 90 96 104 110 116 140 170	67191546516
SPT(14)	404015071990743557	0 54 66 80 110 114 116 120 122 126 156 170 182 236	82118246586
SPT(14)	404015072852255483	0 14 54 80 98 104 146 168 210 216 234 260 300 314	82979758512