Prime p₀= 2286412419563249837 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 112 2 64 2 10 2 10 2 16 2 (?)
a_n: 0 2 30 32 144 146 210 212 222 224 234 236 252 254
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: 254
Found by: rlacr
db: batch=81, k=14, 28 112 64 10 10 16

SPT(16)	2286411037437104191	0 18 40 66 96 102 108 120 238 250 256 262 292 318 340 358	-1382126145646
SPT(16)	2286411064866859969	0 22 42 54 100 154 190 220 294 324 360 414 460 472 492 514	-1354696389868
SPT(16)	2286411312390918101	0 32 102 116 158 168 212 228 320 336 380 390 432 446 516 548	-1107172331736
TPT(14)	2286411362386790381	0 2 30 32 246 248 378 380 420 422 546 548 600 602	-1057176459456
SPT(16)	2286411446428603253	0 44 48 60 90 110 114 138 146 170 174 194 224 236 240 284	-973134646584
SPT(16)	2286412208240040323	0 14 20 24 36 48 66 98 126 158 176 188 200 204 210 224	-211323209514
SPT(16)	2286412567457590643	0 24 38 84 128 134 158 170 198 210 234 240 284 330 344 368	147894340806
SPT(16)	2286412699889172707	0 2 20 66 72 74 110 144 152 186 222 224 230 276 294 296	280325922870
SPT(16)	2286412876191740911	0 6 28 30 70 72 96 108 160 172 196 198 238 240 262 268	456628491074
SPT(16)	2286413785791300427	0 34 42 54 70 120 124 132 184 192 196 246 262 274 282 316	1366228050590
TPT(16)	2286413830233569039	0 2 48 50 78 80 90 92 120 122 150 152 168 170 210 212	1410670319202