Prime p₀= 2865126346761364709 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 40 2 10 2 28 2 286 2 16 2 (?)
a_n: 0 2 48 50 90 92 102 104 132 134 420 422 438 440
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: 440
Found by: [SG]ATA-Rolf
db: batch=82, k=14, 46 40 10 28 286 16

STPT(10)	2865123609288467027	0 2 12 14 72 74 132 134 144 146	-2737472897682
SPT(16)	2865123616719991951	0 16 18 36 70 100 112 130 168 186 198 228 262 280 282 298	-2730041372758
SPT(16)	2865125283535247981	0 6 50 68 78 86 110 180 206 276 300 308 318 336 380 386	-1063226116728
SPT(16)	2865125286847538851	0 10 12 22 78 96 156 178 210 232 292 310 366 376 378 388	-1059913825858
STPT(10)	2865125396680580741	0 2 36 38 78 80 120 122 156 158	-950080783968
TPT(14)	2865125796395631017	0 2 30 32 72 74 144 146 252 254 480 482 504 506	-550365733692
SPT(16)	2865126644776692287	0 6 24 50 66 80 84 96 104 116 120 134 150 176 194 200	298015327578
SPT(16)	2865126650677772837	0 6 14 20 102 126 144 170 186 212 230 254 336 342 350 356	303916408128
SPT(16)	2865126662023457033	0 14 44 54 96 156 206 210 224 228 278 338 380 390 420 434	315262092324
TPT(14)	2865127075679017781	0 2 30 32 126 128 168 170 210 212 228 230 288 290	728917653072
SPT(16)	2865127252437797297	0 14 26 30 66 74 110 122 144 156 192 200 236 240 252 266	905676432588