Prime p₀= 2533457011590928601 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 10 2 76 2 118 2 28 2 22 2 (?)
a_n: 0 2 36 38 48 50 126 128 246 248 276 278 300 302
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: 302
Found by: [SG]ATA-Rolf
db: batch=82, k=14, 34 10 76 118 28 22

STPT(10)	2533453849491907007	0 2 30 32 42 44 54 56 84 86	-3162099021594
SPT(16)	2533453984592779163	0 6 18 38 48 54 60 80 84 104 110 116 126 146 158 164	-3026998149438
STPT(10)	2533454838336877121	0 2 6 8 18 20 30 32 36 38	-2173254051480
STPT(10)	2533455749530286039	0 2 18 20 30 32 42 44 60 62	-1262060642562
SPT(16)	2533456731742309333	0 30 46 94 100 168 178 220 234 276 286 354 360 408 424 454	-279848619268
SPT(16)	2533456975450296029	0 8 60 134 140 162 164 168 194 198 200 222 228 302 354 362	-36140632572
STPT(10)	2533457165896486631	0 2 6 8 48 50 90 92 96 98	154305558030
SPT(16)	2533457513844476789	0 14 48 84 122 140 182 198 224 240 282 300 338 374 408 422	502253548188
TPT(14)	2533457623416162629	0 2 60 62 132 134 168 170 180 182 270 272 300 302	611825234028
SPT(16)	2533457893120026683	0 6 30 56 84 90 150 200 264 314 374 380 408 434 458 464	881529098082
STPT(10)	2533458738810198971	0 2 36 38 78 80 120 122 156 158	1727219270370