Prime p₀= 567540594944513171 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 76 2 40 2 4 2 28 2 40 2 (?)
a_n: 0 2 78 80 120 122 126 128 156 158 198 200
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: gemini8
db: batch=71, k=12, 76 40 4 28 40

SPT(14)	567540526975788721	0 6 40 60 88 90 106 192 208 210 238 258 292 298	-67968724450
TPT(12)	567540552520603721	0 2 78 80 90 92 120 122 168 170 180 182	-42423909450
SPT(14)	567540552859746541	0 12 28 60 108 132 136 162 166 190 238 270 286 298	-42084766630
SPT(14)	567540578699045311	0 6 28 52 66 90 96 112 118 142 156 180 202 208	-16245467860
SPT(14)	567540583257557303	0 8 14 18 38 60 78 80 98 120 140 144 150 158	-11686955868
SPT(14)	567540584001839779	0 22 24 64 84 88 114 148 174 178 198 238 240 262	-10942673392
TPT(12)	567540595946708687	0 2 90 92 114 116 120 122 132 134 144 146	1002195516
SPT(14)	567540611336172889	0 18 34 78 88 148 154 204 210 270 280 324 340 358	16391659718
TPT(12)	567540618868873631	0 2 18 20 48 50 120 122 210 212 330 332	23924360460
SPT(14)	567540642293801801	0 50 66 72 108 126 150 218 242 260 296 302 318 368	47349288630
SPT(14)	567540652174108021	0 12 22 58 82 100 112 126 138 156 180 216 226 238	57229594850