Prime p₀= 2344606737494617571 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 16 2 40 2 10 2 16 2 10 2 (?)
a_n: 0 2 48 50 66 68 108 110 120 122 138 140 150 152
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: 152
Found by: Landjunge
db: batch=81, k=14, 46 16 40 10 16 10

SPT(16)	2344605182927919251	0 2 6 20 36 60 86 140 162 216 242 266 282 296 300 302	-1554566698320
STPT(10)	2344605565332334061	0 2 6 8 18 20 30 32 36 38	-1172162283510
STPT(10)	2344605657660834107	0 2 72 74 222 224 372 374 444 446	-1079833783464
STPT(10)	2344605679461930551	0 2 6 8 18 20 30 32 36 38	-1058032687020
STPT(10)	2344606241629398077	0 2 90 92 102 104 114 116 204 206	-495865219494
STPT(10)	2344606425630198641	0 2 6 8 18 20 30 32 36 38	-311864418930
SPT(16)	2344607043203183051	0 2 30 42 60 66 80 116 156 192 206 212 230 242 270 272	305708565480
SPT(16)	2344607497278304463	0 6 36 104 204 216 230 234 266 270 284 296 396 464 494 500	759783686892
TPT(14)	2344607726766364469	0 2 12 14 60 62 102 104 168 170 300 302 390 392	989271746898
TPT(14)	2344608021871129757	0 2 12 14 42 44 72 74 114 116 210 212 264 266	1284376512186
SPT(16)	2344608049046153179	0 60 70 142 144 154 174 214 240 280 300 310 312 384 394 454	1311551535608