Prime p₀= 510409085249449667 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 28 2 40 2 106 2 40 2 16 2 (?)
a_n: 0 2 30 32 72 74 180 182 222 224 240 242
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: 242
Found by: Dr Who Fan
db: batch=71, k=12, 28 40 106 40 16

SPT(16)	510409030961089177	0 4 10 16 22 36 42 52 114 124 130 144 150 156 162 166	-54288360490
SPT(14)	510409032547771391	0 38 56 72 86 156 170 228 242 312 326 342 360 398	-52701678276
SPT(14)	510409036569104251	0 12 18 40 78 96 102 106 112 130 168 190 196 208	-48680345416
SPT(14)	510409043186882347	0 4 30 84 100 126 172 264 310 336 352 406 432 436	-42062567320
TPT(12)	510409061996659919	0 2 60 62 90 92 210 212 228 230 240 242	-23252789748
SPT(14)	510409073993578223	0 18 36 60 78 80 98 126 144 146 164 188 206 224	-11255871444
SPT(14)	510409092677139379	0 12 42 132 142 208 240 250 282 348 358 448 478 490	7427689712
TPT(12)	510409105848708881	0 2 6 8 78 80 90 92 168 170 216 218	20599259214
SPT(14)	510409113990523093	0 10 34 36 66 78 118 156 196 208 238 240 264 274	28741073426
SPT(14)	510409131466307947	0 4 30 40 70 96 100 180 184 210 240 250 276 280	46216858280
SPT(14)	510409182906092179	0 30 48 52 54 94 100 132 138 178 180 184 202 232	97656642512