Prime p₀= 408434154227206337 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 22 2 124 2 28 2 10 2 40 2 (?)
a_n: 0 2 24 26 150 152 180 182 192 194 234 236
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: 236
Found by: Cruncher Pete
db: batch=70, k=12, 22 124 28 10 40

SPT(14)	408433999554436789	0 70 124 138 162 190 198 244 252 280 304 318 372 442	-154672769548
SPT(14)	408434075613865811	0 38 126 132 168 188 206 342 360 380 416 422 510 548	-78613340526
SPT(14)	408434083392163979	0 68 72 90 120 132 150 152 170 182 212 230 234 302	-70835042358
SPT(14)	408434107287014339	0 12 18 24 42 68 104 108 144 170 188 194 200 212	-46940191998
SPT(14)	408434115418084487	0 26 54 72 84 114 120 176 182 212 224 242 270 296	-38809121850
SPT(14)	408434141609952167	0 50 80 92 110 134 152 162 180 204 222 234 264 314	-12617254170
TPT(12)	408434170416060287	0 2 72 74 90 92 102 104 174 176 204 206	16188853950
SPT(14)	408434221989452389	0 42 64 70 112 150 168 184 202 240 282 288 310 352	67762246052
SPT(14)	408434223064888681	0 16 58 78 118 136 138 178 180 198 238 258 300 316	68837682344
SPT(14)	408434224935672053	0 48 54 66 96 98 104 150 156 158 188 200 206 254	70708465716
SPT(14)	408434271080911633	0 28 34 60 78 88 108 130 150 160 178 204 210 238	116853705296