Prime p₀= 408610442552583317 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 112 2 16 2 46 2 28 2 10 2 (?)
a_n: 0 2 114 116 132 134 180 182 210 212 222 224
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: 224
Found by: Cruncher Pete
db: batch=70, k=12, 112 16 46 28 10

SPT(14)	408610302257854063	0 34 54 66 76 100 160 174 234 258 268 280 300 334	-140294729254
SPT(14)	408610333931998369	0 124 142 168 184 294 300 352 358 468 484 510 528 652	-108620584948
SPT(14)	408610361738283437	0 6 50 54 74 96 102 134 140 162 182 186 230 236	-80814299880
SPT(14)	408610375326838123	0 28 60 66 84 96 106 108 118 130 148 154 186 214	-67225745194
SPT(14)	408610413958437529	0 24 54 60 88 108 130 132 154 174 202 208 238 262	-28594145788
SPT(14)	408610437122144581	0 22 52 60 70 88 102 136 150 168 178 186 216 238	-5430438736
SPT(14)	408610454634371683	0 18 64 78 88 130 154 180 204 246 256 270 316 334	12081788366
SPT(14)	408610464346161841	0 10 18 36 78 100 108 148 156 178 220 238 246 256	21793578524
SPT(13)	408610465140751259	0 12 42 84 114 144 162 180 210 240 282 312 324	22588167942
SPT(14)	408610465784263577	0 6 24 60 66 90 120 170 200 224 230 266 284 290	23231680260
SPT(14)	408610502892334387	0 42 46 52 54 72 94 102 124 142 144 150 154 196	60339751070