Prime p₀= 2045626050780129581 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 130 2 28 2 118 2 4 2 40 2 (?)
a_n: 0 2 78 80 210 212 240 242 360 362 366 368 408 410
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: 410
Found by: Landjunge
db: batch=80, k=14, 76 130 28 118 4 40

SPT(16)	2045624350657347671	0 8 38 68 72 92 122 150 170 198 228 248 252 282 312 320	-1700122781910
STPT(10)	2045624485846615517	0 2 30 32 42 44 54 56 84 86	-1564933514064
SPT(16)	2045624718958139773	0 46 70 76 130 160 174 226 324 376 390 420 474 480 504 550	-1331821989808
STPT(10)	2045624996285171069	0 2 18 20 30 32 42 44 60 62	-1054494958512
SPT(13)	2045625157564275251	0 6 30 60 72 132 156 180 240 252 282 306 312	-893215854330
STPT(10)	2045625349814928821	0 2 30 32 60 62 90 92 120 122	-700965200760
SPT(16)	2045626107572660819	0 72 104 180 204 222 230 302 342 414 422 440 464 540 572 644	56792531238
SPT(16)	2045626371769107709	0 88 150 162 168 190 214 234 268 288 312 334 340 352 414 502	320988978128
SPT(16)	2045626476818793983	0 6 36 38 56 60 74 86 288 300 314 318 336 338 368 374	426038664402
SPT(16)	2045626484592698849	0 24 50 62 80 84 140 188 234 282 338 342 360 372 398 422	433812569268
SPT(16)	2045626694203588537	0 16 30 34 40 66 84 100 126 142 160 186 192 196 210 226	643423458956