Prime p₀= 2159202674182298201 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 46 2 76 2 58 2 22 2 4 2 (?)
a_n: 0 2 30 32 78 80 156 158 216 218 240 242 246 248
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: 248
Found by: rlacr
db: batch=81, k=14, 28 46 76 58 22 4

SPT(16)	2159200665609436147	0 4 12 46 100 102 196 222 244 270 364 366 420 454 462 466	-2008572862054
SPT(16)	2159201154869990899	0 30 54 84 108 114 118 142 150 174 178 184 208 238 262 292	-1519312307302
TPT(14)	2159201435749196549	0 2 60 62 138 140 168 170 228 230 240 242 258 260	-1238433101652
SPT(16)	2159201711043350329	0 24 30 72 90 118 124 168 184 228 234 262 280 322 328 352	-963138947872
TPT(14)	2159202190106390657	0 2 114 116 132 134 282 284 324 326 384 386 390 392	-484075907544
STPT(10)	2159202607804598537	0 2 24 26 42 44 60 62 84 86	-66377699664
SPT(16)	2159202697628089189	0 40 70 94 102 118 138 174 178 214 234 250 258 282 312 352	23445790988
SPT(16)	2159202748427600069	0 24 38 54 74 80 102 120 122 140 162 168 188 204 218 242	74245301868
SPT(16)	2159202814490888773	0 6 18 28 34 78 84 168 256 340 346 390 396 406 418 424	140308590572
SPT(16)	2159202832308315641	0 18 78 92 96 212 222 228 260 266 276 392 396 410 470 488	158126017440
SPT(16)	2159202911659587559	0 12 28 52 82 94 132 142 150 160 198 210 240 264 280 292	237477289358