Prime p₀= 561758920364891111 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 16 2 100 2 34 2 28 2 70 2 (?)
a_n: 0 2 18 20 120 122 156 158 186 188 258 260
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: 260
Found by: Rantanplan
db: batch=71, k=12, 16 100 34 28 70

SPT(14)	561758831568061861	0 16 48 66 88 96 108 118 130 138 160 178 210 226	-88796829250
SPT(14)	561758837686656941	0 2 36 56 90 122 168 170 216 248 282 302 336 338	-82678234170
TPT(12)	561758847821534969	0 2 72 74 102 104 138 140 180 182 348 350	-72543356142
SPT(14)	561758879263559179	0 4 10 42 54 70 82 102 114 130 142 174 180 184	-41101331932
SPT(14)	561758884917356279	0 2 48 72 84 104 152 270 318 338 350 374 420 422	-35447534832
TPT(12)	561758901907803161	0 2 198 200 258 260 288 290 300 302 336 338	-18457087950
SPT(14)	561758951385369571	0 16 40 52 66 130 150 172 192 256 270 282 306 322	31020478460
TPT(12)	561758965312718207	0 2 24 26 84 86 102 104 144 146 150 152	44947827096
TPT(12)	561758972588908691	0 2 18 20 48 50 78 80 210 212 216 218	52224017580
SPT(14)	561758976109657621	0 36 66 72 78 102 148 150 196 220 226 232 262 298	55744766510
SPT(14)	561758976341439367	0 12 30 106 126 142 232 324 414 430 450 526 544 556	55976548256