Prime p₀= 24312570516391121 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 16 2 10 2 64 2 28 2 70 2 (?)
a_n: 0 2 18 20 30 32 96 98 126 128 198 200
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: 200
Found by: Dario666
db: batch=65, k=12, 16 10 64 28 70

SPT(16)	24312526866563123	0 30 38 48 66 126 140 144 170 174 188 248 266 276 284 314	-43649827998
STPT(10)	24312534966210311	0 2 6 8 18 20 30 32 36 38	-35550180810
SPT(14)	24312537028372181	0 12 18 72 92 102 120 158 176 186 206 260 266 278	-33488018940
SPT(14)	24312541760959849	0 48 64 82 118 148 192 220 264 294 330 348 364 412	-28755431272
SPT(14)	24312546826416581	0 32 66 80 102 140 150 152 162 200 222 236 270 302	-23689974540
STPT(10)	24312556921345877	0 2 30 32 60 62 90 92 120 122	-13595045244
SPT(14)	24312575817291481	0 18 88 96 100 102 142 156 196 198 202 210 280 298	5300900360
TPT(12)	24312583459233269	0 2 72 74 102 104 132 134 210 212 222 224	12942842148
SPT(14)	24312584596813111	0 16 36 46 48 60 70 78 88 100 102 112 132 148	14080421990
SPT(14)	24312587000464601	0 2 12 20 26 48 62 66 80 102 108 116 126 128	16484073480
SPT(14)	24312587898815771	0 8 20 78 92 132 146 162 176 216 230 288 300 308	17382424650