Prime p₀= 3008826182569022357 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 40 2 88 2 4 2 40 2 28 2 (?)
a_n: 0 2 42 44 84 86 174 176 180 182 222 224 252 254
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: 254
Found by: Orange Kid
db: batch=82, k=14, 40 40 88 4 40 28

SPT(16)	3008825321271881509	0 10 24 60 84 88 118 124 144 150 180 184 208 244 258 268	-861297140848
SPT(16)	3008825541199467659	0 50 90 120 134 164 222 230 264 272 330 360 374 404 444 494	-641369554698
STPT(10)	3008825545616123291	0 2 36 38 78 80 120 122 156 158	-636952899066
TPT(14)	3008825947726655039	0 2 18 20 60 62 102 104 222 224 228 230 300 302	-234842367318
STPT(10)	3008825995408517651	0 2 6 8 48 50 90 92 96 98	-187160504706
SPT(16)	3008826082999792859	0 42 44 110 138 152 174 182 240 248 270 284 312 378 380 422	-99569229498
TPT(14)	3008826521769938069	0 2 72 74 198 200 258 260 300 302 420 422 468 470	339200915712
STPT(10)	3008826549248837027	0 2 42 44 72 74 102 104 144 146	366679814670
STPT(10)	3008826649689204737	0 2 30 32 42 44 54 56 84 86	467120182380
SPT(16)	3008826731153663873	0 6 50 56 68 74 78 96 98 116 120 126 138 144 188 194	548584641516
SPT(16)	3008826802292184281	0 48 50 72 90 132 146 168 170 192 206 248 266 288 290 338	619723161924