Prime p₀= 3086331126676964951 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 40 2 28 2 58 2 106 2 28 2 (?)
a_n: 0 2 36 38 78 80 108 110 168 170 276 278 306 308
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: 308
Found by: [SG-2W]Kurzer
db: batch=83, k=14, 34 40 28 58 106 28

SPT(16)	3086328931433859851	0 20 60 68 120 150 152 180 230 258 260 290 342 350 390 410	-2195243105100
SPT(18)	3086329006715014777	0 12 36 66 70 72 90 94 124 192 222 226 244 246 250 280 304 316	-2119961950174
SPT(16)	3086329767161734831	0 40 106 108 136 156 168 246 280 358 370 390 418 420 486 526	-1359515230120
STPT(10)	3086329770220843511	0 2 30 32 78 80 126 128 156 158	-1356456121440
TPT(14)	3086330085948965039	0 2 18 20 30 32 42 44 72 74 120 122 240 242	-1040727999912
SPT(16)	3086330339923063511	0 20 42 56 78 80 98 146 222 270 288 290 312 326 348 368	-786753901440
TPT(14)	3086331644127981857	0 2 54 56 180 182 210 212 282 284 312 314 324 326	517451016906
TPT(14)	3086332044319146977	0 2 30 32 72 74 90 92 102 104 132 134 144 146	917642182026
SPT(16)	3086332078800328031	0 6 50 60 72 78 98 120 128 150 170 176 188 198 242 248	952123363080
STPT(10)	3086332185412651991	0 2 6 8 48 50 90 92 96 98	1058735687040
STPT(10)	3086333584930863887	0 2 42 44 72 74 102 104 144 146	2458253898936