Prime p₀= 2256726524423326181 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 58 2 28 2 34 2 112 2 16 2 (?)
a_n: 0 2 30 32 90 92 120 122 156 158 270 272 288 290
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: 290
Found by: Orange Kid
db: batch=81, k=14, 28 58 28 34 112 16

SPT(16)	2256725443413194009	0 2 50 72 110 144 152 210 254 312 320 354 392 414 462 464	-1081010132172
SPT(16)	2256725508822303049	0 4 18 100 130 138 154 172 180 198 214 222 252 334 348 352	-1015601023132
SPT(16)	2256725715350587367	0 74 102 150 152 164 182 206 210 234 252 264 266 314 342 416	-809072738814
STPT(10)	2256725808805868297	0 2 60 62 102 104 144 146 204 206	-715617457884
TPT(14)	2256726053601144467	0 2 24 26 84 86 210 212 222 224 264 266 312 314	-470822181714
SPT(16)	2256726416924564441	0 36 80 86 182 198 252 258 290 296 350 366 462 468 512 548	-107498761740
SPT(18)	2256726661387780541	0 32 56 68 98 102 110 152 212 276 336 378 386 390 420 432 456 488	136964454360
STPT(10)	2256726952364807957	0 2 60 62 72 74 84 86 144 146	427941481776
TPT(14)	2256727260268951271	0 2 6 8 18 20 48 50 90 92 168 170 216 218	735845625090
SPT(16)	2256727373620642261	0 6 16 30 48 72 78 150 328 400 406 430 448 462 472 478	849197316080
SPT(16)	2256727477963676717	0 200 206 236 266 270 282 296 336 350 362 366 396 426 432 632	953540350536