Prime p₀= 4044339130205238329 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 142 2 64 2 58 2 28 2 22 2 (?)
a_n: 0 2 48 50 192 194 258 260 318 320 348 350 372 374
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: 374
Found by: Asgard2022
db: batch=84, k=14, 46 142 64 58 28 22

STPT(10)	4044338045005522679	0 2 18 20 30 32 42 44 60 62	-1085199715650
SPT(16)	4044338161564980523	0 18 24 28 46 58 210 226 228 244 396 408 426 430 436 454	-968640257806
STPT(10)	4044338180225726309	0 2 12 14 90 92 168 170 180 182	-949979512020
SPT(16)	4044338410589027767	0 6 12 24 52 82 100 132 244 276 294 324 352 364 370 376	-719616210562
SPT(16)	4044338531568166801	0 12 22 40 72 78 100 112 198 210 232 238 270 288 298 310	-598637071528
STPT(10)	4044338776437811739	0 2 18 20 30 32 42 44 60 62	-353767426590
TPT(14)	4044339131842099967	0 2 42 44 60 62 114 116 132 134 204 206 270 272	1636861638
SPT(16)	4044339350458406017	0 42 64 124 132 142 154 184 222 252 264 274 282 342 364 406	220253167688
STPT(10)	4044339483542339711	0 2 36 38 78 80 120 122 156 158	353337101382
SPT(16)	4044339610622793931	0 22 28 60 78 120 138 208 252 322 340 382 400 432 438 460	480417555602
STPT(10)	4044339738059615549	0 2 42 44 60 62 78 80 120 122	607854377220