Prime p₀= 288791261935248089 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 10 2 28 2 64 2 28 2 40 2 (?)
a_n: 0 2 12 14 42 44 108 110 138 140 180 182
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: 182
Found by: [AF>Amis des Lapins] Ceclo
db: batch=69, k=12, 10 28 64 28 40

SPT(14)	288791189548359209	0 20 38 60 140 144 150 182 188 192 272 294 312 332	-72386888880
SPT(14)	288791202013453277	0 6 12 26 42 80 132 320 372 410 426 440 446 452	-59921794812
SPT(14)	288791208564393091	0 22 40 42 58 60 72 88 100 102 118 120 138 160	-53370854998
SPT(14)	288791209837114519	0 12 22 28 52 58 82 108 132 138 162 168 178 190	-52098133570
SPT(14)	288791244251380289	0 24 38 42 68 90 104 108 122 144 170 174 188 212	-17683867800
SPT(16)	288791261786839489	0 28 34 42 54 88 124 130 132 138 174 208 220 228 234 262	-148408600
SPT(14)	288791272782142357	0 6 22 24 52 90 120 196 226 264 292 294 310 316	10846894268
TPT(12)	288791291914141361	0 2 36 38 78 80 90 92 156 158 168 170	29978893272
SPT(14)	288791296423242881	0 8 30 42 60 78 108 140 170 188 206 218 240 248	34487994792
TPT(12)	288791297983821977	0 2 84 86 114 116 120 122 180 182 210 212	36048573888
SPT(14)	288791339074986487	0 4 12 102 112 136 154 192 210 234 244 334 342 346	77139738398