Prime p₀= 568823589720479747 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 82 2 4 2 28 2 40 2 10 2 (?)
a_n: 0 2 84 86 90 92 120 122 162 164 174 176
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: 176
Found by: engiefox
db: batch=71, k=12, 82 4 28 40 10

SPT(14)	568823491405692781	0 30 58 82 96 102 118 390 406 412 426 450 478 508	-98314786966
SPT(14)	568823529543342859	0 34 60 78 88 90 100 132 142 144 154 172 198 232	-60177136888
SPT(14)	568823552967441883	0 30 34 100 150 154 160 174 180 184 234 300 304 334	-36753037864
SPT(14)	568823576149159489	0 4 12 22 28 54 64 78 88 114 120 130 138 142	-13571320258
SPT(14)	568823581760243609	0 30 90 128 132 140 158 174 192 200 204 242 302 332	-7960236138
TPT(12)	568823583125831939	0 2 48 50 78 80 120 122 180 182 300 302	-6594647808
SPT(14)	568823603265802583	0 18 24 66 86 140 150 164 174 228 248 290 296 314	13545322836
SPT(14)	568823626039379261	0 6 18 50 56 62 68 90 96 102 108 140 152 158	36318899514
SPT(14)	568823654576806463	0 24 44 50 66 80 84 86 90 104 120 126 146 170	64856326716
SPT(14)	568823674077779137	0 30 54 64 72 94 114 190 210 232 240 250 274 304	84357299390
SPT(14)	568823693314865539	0 124 132 162 178 180 192 220 232 234 250 280 288 412	103594385792