Prime p₀= 415741522714410551 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 34 2 28 2 70 2 16 2 22 2 (?)
a_n: 0 2 36 38 66 68 138 140 156 158 180 182
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: 182
Found by: Cruncher Pete
db: batch=70, k=12, 34 28 70 16 22

SPT(14)	415741417129673039	0 20 42 54 80 98 104 108 114 132 158 170 192 212	-105584737512
SPT(14)	415741423869710899	0 42 52 90 100 120 132 178 190 210 220 258 268 310	-98844699652
SPT(14)	415741427067676573	0 28 64 66 94 108 120 184 196 210 238 240 276 304	-95646733978
SPT(14)	415741473078901309	0 64 118 124 148 168 174 244 250 270 294 300 354 418	-49635509242
SPT(14)	415741479908574151	0 28 48 52 70 90 96 112 118 138 156 160 180 208	-42805836400
SPT(14)	415741502360409307	0 24 42 52 66 76 84 112 120 130 144 154 172 196	-20354001244
SPT(14)	415741540119212509	0 10 24 72 82 90 100 252 262 270 280 328 342 352	17404801958
SPT(14)	415741543758989821	0 18 48 70 72 102 156 172 226 256 258 280 310 328	21044579270
SPT(14)	415741571968196863	0 16 30 36 78 100 120 166 186 208 250 256 270 286	49253786312
TPT(14)	415741574354327237	0 2 30 32 42 44 252 254 282 284 414 416 420 422	51639916686
SPT(14)	415741576605021811	0 46 60 70 202 222 232 270 280 300 432 442 456 502	53890611260