Prime p₀= 2367426154192090931 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 22 2 16 2 136 2 22 2 16 2 (?)
a_n: 0 2 36 38 60 62 78 80 216 218 240 242 258 260
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: 260
Found by: [SG-2W]Kurzer
db: batch=81, k=14, 34 22 16 136 22 16

SPT(13)	2367424745866202419	0 18 24 60 78 108 144 180 210 228 264 270 288	-1408325888512
SPT(16)	2367424774097211611	0 18 26 110 126 138 168 198 308 338 368 380 396 480 488 506	-1380094879320
SPT(16)	2367424958037158141	0 20 36 38 50 68 72 90 128 146 150 168 180 182 198 218	-1196154932790
SPT(16)	2367425101919499841	0 16 18 58 70 72 150 156 172 178 256 258 270 310 312 328	-1052272591090
SPT(16)	2367425421844072571	0 20 42 56 78 86 102 132 326 356 372 380 402 416 438 458	-732348018360
SPT(16)	2367425775427447871	0 8 12 30 48 66 78 92 126 140 152 170 188 206 210 218	-378764643060
STPT(10)	2367426474526126199	0 2 18 20 30 32 42 44 60 62	320334035268
STPT(10)	2367426617550465347	0 2 30 32 60 62 90 92 120 122	463358374416
SPT(16)	2367426784683407753	0 18 38 126 194 210 224 270 314 360 374 390 458 546 566 584	630491316822
SPT(13)	2367426911587855189	0 24 48 108 114 168 234 300 354 360 420 444 468	757395764258
TPT(14)	2367427245914128631	0 2 36 38 60 62 156 158 228 230 258 260 270 272	1091722037700