Prime p₀= 2338628372574589217 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 28 2 136 2 22 2 94 2 40 2 (?)
a_n: 0 2 12 14 42 44 180 182 204 206 300 302 342 344
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: 344
Found by: Landjunge
db: batch=81, k=14, 10 28 136 22 94 40

SPT(16)	2338627600195401653	0 6 108 146 168 180 210 224 270 284 314 326 348 386 488 494	-772379187564
SPT(16)	2338627600286582063	0 30 60 68 78 84 96 98 156 158 170 176 186 194 224 254	-772288007154
SPT(16)	2338627671565179341	0 20 36 42 78 86 98 120 188 210 222 230 266 272 288 308	-701009409876
SPT(16)	2338627796873345891	0 2 20 60 110 132 140 188 222 270 278 300 350 390 408 410	-575701243326
SPT(16)	2338627797183564031	0 22 28 36 66 70 208 246 292 330 468 472 502 510 516 538	-575391025186
TPT(14)	2338628253550261061	0 2 6 8 30 32 336 338 450 452 516 518 576 578	-119024328156
SPT(16)	2338628917907130521	0 38 98 110 156 170 180 248 270 338 348 362 408 420 480 518	545332541304
STPT(10)	2338629583037668979	0 2 42 44 60 62 78 80 120 122	1210463079762
SPT(16)	2338629823249593257	0 44 54 66 72 80 104 140 156 192 216 224 230 242 252 296	1450675004040
STPT(10)	2338629827256903161	0 2 36 38 78 80 120 122 156 158	1454682313944
STPT(10)	2338629923669971541	0 2 36 38 78 80 120 122 156 158	1551095382324