Prime p₀= 2949191148309870251 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 106 2 28 2 46 2 52 2 28 2 (?)
a_n: 0 2 30 32 138 140 168 170 216 218 270 272 300 302
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: 302
Found by: Landjunge
db: batch=82, k=14, 28 106 28 46 52 28

SPT(16)	2949190142076888019	0 10 34 48 52 78 114 150 202 238 274 300 304 318 342 352	-1006232982232
SPT(16)	2949190160692160857	0 16 40 42 72 106 124 156 190 222 240 274 304 306 330 346	-987617709394
SPT(16)	2949190189605968537	0 32 36 62 104 146 152 246 290 384 390 432 474 500 504 536	-958703901714
TPT(14)	2949190533003595787	0 2 60 62 90 92 132 134 210 212 240 242 294 296	-615306274464
SPT(16)	2949190728237503039	0 2 24 38 50 54 68 140 162 234 248 252 264 278 300 302	-420072367212
SPT(16)	2949190882017866903	0 14 18 36 86 128 140 156 158 174 186 228 278 296 300 314	-266292003348
SPT(16)	2949191160382218319	0 12 18 22 40 60 78 102 130 154 172 192 210 214 220 232	12072348068
SPT(16)	2949191262709970923	0 28 30 144 198 274 276 298 456 478 480 556 610 724 726 754	114400100672
TPT(14)	2949191491001105489	0 2 12 14 18 20 42 44 102 104 168 170 198 200	342691235238
SPT(16)	2949191761855276061	0 56 78 98 120 138 146 182 186 222 230 248 270 290 312 368	613545405810
SPT(16)	2949191839735858403	0 30 36 120 198 266 320 326 390 396 450 518 596 680 686 716	691425988152