Prime p₀= 115691233626601781 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 28 2 4 2 40 2 28 2 40 2 (?)
a_n: 0 2 30 32 36 38 78 80 108 110 150 152
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: 152
Found by: nenym
db: batch=67, k=12, 28 4 40 28 40

SPT(14)	115691170491079769	0 14 32 108 134 144 150 302 308 318 344 420 438 452	-63135522012
SPT(14)	115691180164854587	0 2 20 30 56 60 66 80 86 90 116 126 144 146	-53461747194
SPT(14)	115691209879230343	0 28 30 40 46 88 96 100 108 150 156 166 168 196	-23747371438
SPT(14)	115691215918967569	0 28 30 34 108 124 130 138 144 160 234 238 240 268	-17707634212
SPT(14)	115691220016936133	0 6 8 20 44 120 140 204 224 300 324 336 338 344	-13609665648
SPT(16)	115691231696907553	0 10 18 66 88 126 144 156 178 190 208 246 268 316 324 334	-1929694228
SPT(14)	115691263955684579	0 74 78 114 120 162 164 198 200 242 248 284 288 362	30329082798
SPT(16)	115691277948996683	0 8 48 114 126 146 150 164 180 194 198 218 230 296 336 344	44322394902
SPT(14)	115691278800335969	0 8 14 24 30 78 90 338 350 398 404 414 420 428	45173734188
SPT(14)	115691297153841403	0 4 100 124 154 166 268 276 378 390 420 444 540 544	63527239622
SPT(14)	115691300980670941	0 12 28 30 42 66 108 130 172 196 208 210 226 238	67354069160