Prime p₀= 2326875373665592991 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 70 2 40 2 106 2 10 2 4 2 (?)
a_n: 0 2 66 68 138 140 180 182 288 290 300 302 306 308
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: Landjunge
db: batch=81, k=14, 64 70 40 106 10 4

TPT(14)	2326873747586657909	0 2 12 14 90 92 162 164 210 212 318 320 432 434	-1626078935082
TPT(14)	2326873978741647407	0 2 72 74 174 176 210 212 282 284 294 296 450 452	-1394923945584
SPT(16)	2326874321535384331	0 22 36 40 42 126 156 208 240 292 322 406 408 412 426 448	-1052130208660
SPT(16)	2326874325119627321	0 26 48 68 98 110 140 146 162 168 198 210 240 260 282 308	-1048545965670
SPT(16)	2326874814870491603	0 14 48 50 98 116 120 146 168 194 198 216 264 266 300 314	-558795101388
SPT(16)	2326875234901884673	0 6 40 48 54 70 76 88 96 108 114 130 136 144 178 184	-138763708318
SPT(16)	2326875639717293309	0 98 140 162 170 182 248 270 302 324 390 402 410 432 474 572	266051700318
SPT(16)	2326875643922876831	0 12 38 42 50 66 78 108 140 170 182 198 206 210 236 248	270257283840
SPT(16)	2326876145533959797	0 24 56 74 84 164 192 206 240 254 282 362 372 390 422 446	771868366806
SPT(16)	2326876441191114457	0 22 36 52 54 106 126 154 222 250 270 322 324 340 354 376	1067525521466
SPT(18)	2326876685408233151	0 18 32 78 86 120 156 162 182 246 266 272 308 342 350 396 410 428	1311742640160