Prime p₀= 2568389646189129767 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 46 2 10 2 28 2 34 2 58 2 (?)
a_n: 0 2 54 56 102 104 114 116 144 146 180 182 240 242
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 242
Found by: RFGuy_KCCO
db: batch=82, k=14, 52 46 10 28 34 58

STPT(10)	2568387354856955519	0 2 18 20 30 32 42 44 60 62	-2291332174248
SPT(16)	2568387656099165443	0 30 154 156 160 166 190 226 228 264 288 294 298 300 424 454	-1990089964324
STPT(10)	2568387695160603059	0 2 78 80 120 122 162 164 240 242	-1951028526708
SPT(16)	2568387788106707249	0 18 20 48 72 128 158 210 242 294 324 380 404 432 434 452	-1858082422518
STPT(10)	2568389054208298439	0 2 18 20 30 32 42 44 60 62	-591980831328
STPT(10)	2568389337451127987	0 2 30 32 42 44 54 56 84 86	-308738001780
STPT(10)	2568390017118912377	0 2 30 32 42 44 54 56 84 86	370929782610
SPT(16)	2568390270466178987	0 30 50 92 96 152 164 174 212 222 234 290 294 336 356 386	624277049220
SPT(16)	2568391256119361317	0 40 42 46 66 120 124 154 162 192 196 250 270 274 276 316	1609930231550
SPT(16)	2568391459727055191	0 56 78 92 126 158 162 180 188 206 210 242 276 290 312 368	1813537925424
SPT(20)	2568391818889047601	0 46 58 60 106 130 150 156 160 168 178 186 190 196 216 240 286 288 300 346	2172699917834