Prime p₀= 505317443014046951 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 34 2 28 2 28 2 40 2 16 2 (?)
a_n: 0 2 36 38 66 68 96 98 138 140 156 158
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: 158
Found by: nenym
db: batch=71, k=12, 34 28 28 40 16

SPT(14)	505317327084582983	0 24 60 78 90 104 150 158 204 218 230 248 284 308	-115929463968
TPT(12)	505317350141528987	0 2 12 14 60 62 72 74 150 152 240 242	-92872517964
SPT(14)	505317365532306791	0 48 66 78 80 116 132 176 192 228 230 242 260 308	-77481740160
SPT(14)	505317369043341277	0 10 16 24 34 52 54 112 114 132 142 150 156 166	-73970705674
SPT(14)	505317386717914819	0 10 58 70 88 90 142 168 220 222 240 252 300 310	-56296132132
SPT(14)	505317417247628057	0 30 56 122 134 186 204 332 350 402 414 480 506 536	-25766418894
SPT(14)	505317451677333649	0 4 12 82 84 120 138 154 172 208 210 280 288 292	8663286698
SPT(14)	505317453080942969	0 12 18 32 62 78 84 158 164 180 210 224 230 242	10066896018
STPT(10)	505317465391663751	0 2 30 32 78 80 126 128 156 158	22377616800
SPT(14)	505317480959416129	0 12 28 42 54 60 82 120 142 148 160 174 190 202	37945369178
SPT(14)	505317490499271563	0 14 18 36 68 78 84 110 116 126 158 176 180 194	47485224612