Prime p₀= 290196096570079079 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 40 2 28 2 4 2 130 2 76 2 (?)
a_n: 0 2 42 44 72 74 78 80 210 212 288 290
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: 290
Found by: desktop64
db: batch=69, k=12, 40 28 4 130 76

SPT(14)	290196042443331811	0 48 66 96 100 118 156 160 198 216 220 250 268 316	-54126747268
SPT(16)	290196070732985299	0 10 12 58 88 108 142 154 168 180 214 234 264 310 312 322	-25837093780
TPT(12)	290196073396690631	0 2 126 128 156 158 186 188 198 200 258 260	-23173388448
TPT(12)	290196073618441259	0 2 12 14 42 44 78 80 90 92 150 152	-22951637820
SPT(14)	290196083236611103	0 6 58 76 84 88 100 144 156 160 168 186 238 244	-13333467976
TPT(12)	290196092884893659	0 2 60 62 90 92 102 104 120 122 162 164	-3685185420
TPT(12)	290196104549432369	0 2 12 14 30 32 72 74 162 164 198 200	7979353290
SPT(14)	290196132476249719	0 4 40 48 70 82 90 172 180 192 214 222 258 262	35906170640
TPT(14)	290196150266015141	0 2 36 38 66 68 78 80 150 152 168 170 210 212	53695936062
SPT(14)	290196175650915647	0 26 54 80 92 114 116 120 122 144 156 182 210 236	79080836568
SPT(14)	290196193552793461	0 10 40 42 118 120 160 198 238 240 316 318 348 358	96982714382