Prime p₀= 2726424508387291529 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 34 2 28 2 88 2 22 2 16 2 (?)
a_n: 0 2 72 74 108 110 138 140 228 230 252 254 270 272
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: 272
Found by: JayPi
db: batch=82, k=14, 70 34 28 88 22 16

SPT(13)	2726423679061902563	0 24 60 84 90 126 150 174 210 216 240 276 300	-829325388966
STPT(10)	2726423857504893101	0 2 6 8 48 50 90 92 96 98	-650882398428
SPT(16)	2726423859044688497	0 2 6 14 24 44 80 92 114 126 162 182 192 200 204 206	-649342603032
SPT(16)	2726423988525478061	0 8 18 30 66 72 78 116 132 170 176 182 218 230 240 248	-519861813468
STPT(10)	2726424141311291381	0 2 36 38 78 80 120 122 156 158	-367076000148
SPT(16)	2726424429299861809	0 18 60 88 94 138 180 204 214 238 280 324 330 358 400 418	-79087429720
SPT(16)	2726424707617726337	0 32 62 66 102 126 134 140 186 192 200 224 260 264 294 326	199230434808
SPT(16)	2726425303042332613	0 10 18 24 46 64 88 96 178 186 210 228 250 256 264 274	794655041084
SPT(16)	2726425486040288603	0 18 26 68 110 120 134 140 174 180 194 204 246 288 296 314	977652997074
TPT(14)	2726425571455711199	0 2 18 20 42 44 48 50 72 74 198 200 222 224	1063068419670
SPT(16)	2726425904052723179	0 14 24 30 54 72 80 84 98 102 110 128 152 158 168 182	1395665431650