Prime p₀= 2290589315724511001 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 64 2 28 2 52 2 28 2 16 2 (?)
a_n: 0 2 30 32 96 98 126 128 180 182 210 212 228 230
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: 230
Found by: Landjunge
db: batch=81, k=14, 28 64 28 52 28 16

SPT(16)	2290587522163126237	0 6 52 60 76 94 142 172 174 204 252 270 286 294 340 346	-1793561384764
SPT(16)	2290587675528422729	0 12 32 54 68 138 198 210 242 254 314 384 398 420 440 452	-1640196088272
SPT(16)	2290588067473626293	0 38 80 150 156 158 200 234 260 294 336 338 344 414 456 494	-1248250884708
SPT(16)	2290588472575633057	0 22 24 72 90 94 126 130 216 220 252 256 274 322 324 346	-843148877944
TPT(14)	2290588515725952257	0 2 54 56 60 62 72 74 102 104 114 116 180 182	-799998558744
STPT(10)	2290588660300416557	0 2 42 44 72 74 102 104 144 146	-655424094444
STPT(10)	2290589435956083257	0 2 30 32 72 74 114 116 144 146	120231572256
STPT(10)	2290589510435007107	0 2 60 62 72 74 84 86 144 146	194710496106
STPT(10)	2290589515483464719	0 2 18 20 30 32 42 44 60 62	199758953718
SPT(16)	2290589700784930609	0 30 54 78 84 100 102 124 168 190 192 208 214 238 262 292	385060419608
SPT(16)	2290589831505912253	0 6 18 58 78 108 118 144 160 186 196 226 246 286 298 304	515781401252