Prime p₀= 509960708900255747 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 28 2 82 2 64 2 40 2 10 2 (?)
a_n: 0 2 30 32 114 116 180 182 222 224 234 236
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: Dirk Broer
db: batch=71, k=12, 28 82 64 40 10

SPT(14)	509960648841922979	0 18 38 60 72 128 152 240 264 320 332 354 374 392	-60058332768
SPT(14)	509960668786749559	0 4 84 112 142 220 228 274 282 360 390 418 498 502	-40113506188
SPT(14)	509960680452008017	0 16 36 40 42 66 72 94 100 124 126 130 150 166	-28448247730
SPT(14)	509960686710578491	0 42 58 70 78 82 112 126 156 160 168 180 196 238	-22189677256
SPT(14)	509960695963105493	0 14 30 60 134 168 200 204 236 270 344 374 390 404	-12937150254
SPT(14)	509960697400446701	0 30 78 92 110 120 126 182 188 198 216 230 278 308	-11499809046
SPT(14)	509960709315188051	0 12 42 56 78 138 152 156 170 230 252 266 296 308	414932304
SPT(14)	509960716798684381	0 72 90 118 142 216 228 250 262 336 360 388 406 478	7898428634
TPT(12)	509960718092548517	0 2 12 14 114 116 144 146 222 224 252 254	9192292770
TPT(12)	509960724276569747	0 2 60 62 192 194 282 284 462 464 492 494	15376314000
SPT(14)	509960727690085831	0 66 70 78 108 132 148 180 196 220 250 258 262 328	18789830084