Prime p₀= 2290561865051717237 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 10 2 88 2 46 2 28 2 40 2 (?)
a_n: 0 2 12 14 24 26 114 116 162 164 192 194 234 236
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: 236
Found by: Landjunge
db: batch=81, k=14, 10 10 88 46 28 40

SPT(16)	2290561068611154673	0 78 88 94 126 136 154 166 258 270 288 298 330 336 346 424	-796440562564
STPT(10)	2290561138825331969	0 2 42 44 60 62 78 80 120 122	-726226385268
SPT(16)	2290561472445220321	0 18 72 88 90 100 118 130 210 222 240 250 252 268 322 340	-392606496916
STPT(12)	2290561571369441327	0 2 12 14 42 44 240 242 270 272 282 284	-293682275910
SPT(16)	2290561758848921783	0 24 128 140 164 200 210 218 486 494 504 540 564 576 680 704	-106202795454
SPT(16)	2290561832912118803	0 20 74 98 126 168 170 186 188 204 206 248 276 300 354 374	-32139598434
SPT(16)	2290562111176960717	0 10 52 76 82 160 214 222 244 252 306 384 390 414 456 466	246125243480
TPT(14)	2290562151893993687	0 2 54 56 90 92 132 134 150 152 210 212 222 224	286842276450
SPT(16)	2290562186869574897	0 6 12 56 86 116 140 144 152 156 180 210 240 284 290 296	321817857660
STPT(10)	2290562354681880437	0 2 54 56 72 74 90 92 144 146	489630163200
SPT(16)	2290562503672009453	0 6 54 108 138 154 174 256 258 340 360 376 406 460 508 514	638620292216