Prime p₀= 2786154883848663557 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 88 2 40 2 160 2 76 2 58 2 (?)
a_n: 0 2 60 62 150 152 192 194 354 356 432 434 492 494
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: 494
Found by: JayPi
db: batch=82, k=14, 58 88 40 160 76 58

SPT(16)	2786153517334369667	0 14 30 42 90 122 140 144 170 174 192 224 272 284 300 314	-1366514293890
SPT(16)	2786153616572693737	0 10 34 40 94 154 186 210 220 244 276 336 390 396 420 430	-1267275969820
STPT(10)	2786153707123447667	0 2 30 32 42 44 54 56 84 86	-1176725215890
STPT(10)	2786153944137262241	0 2 6 8 48 50 90 92 96 98	-939711401316
SPT(16)	2786154099335333591	0 2 12 50 72 86 90 120 152 182 186 200 222 260 270 272	-784513329966
SPT(16)	2786154423511714813	0 6 18 34 60 84 96 126 178 208 220 244 270 286 298 304	-460336948744
SPT(16)	2786155044609733843	0 34 40 46 154 160 166 180 244 258 264 270 378 384 390 424	160761070286
SPT(16)	2786155083029972977	0 22 42 82 112 136 144 162 214 232 240 264 294 334 354 376	199181309420
TPT(14)	2786155234404292769	0 2 30 32 72 74 198 200 228 230 462 464 468 470	350555629212
SPT(16)	2786155272789642731	0 20 48 68 90 96 102 116 132 146 152 158 180 200 228 248	388940979174
STPT(10)	2786155464120223397	0 2 42 44 72 74 102 104 144 146	580271559840