Prime p₀= 2338443283464848687 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 58 2 88 2 154 2 10 2 70 2 (?)
a_n: 0 2 54 56 114 116 204 206 360 362 372 374 444 446
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: 446
Found by: sabres1616
db: batch=81, k=14, 52 58 88 154 10 70

SPT(18)	2338442344385657077	0 52 72 96 106 154 184 192 250 306 364 372 402 450 460 484 504 556	-939079191610
STPT(10)	2338442470567332011	0 2 36 38 78 80 120 122 156 158	-812897516676
SPT(16)	2338442482965943951	0 6 10 28 42 48 76 78 100 102 130 136 150 168 172 178	-800498904736
SPT(16)	2338442731189636627	0 6 24 30 34 90 112 142 174 204 226 282 286 292 310 316	-552275212060
STPT(10)	2338442882304251531	0 2 6 8 48 50 90 92 96 98	-401160597156
SPT(16)	2338442908740533627	0 6 32 86 116 120 140 174 182 216 236 240 270 324 350 356	-374724315060
STPT(10)	2338443486808651721	0 2 36 38 78 80 120 122 156 158	203343803034
STPT(10)	2338443593490325301	0 2 30 32 78 80 126 128 156 158	310025476614
STPT(10)	2338443916594100069	0 2 18 20 30 32 42 44 60 62	633129251382
TPT(14)	2338443924188050517	0 2 12 14 60 62 114 116 144 146 222 224 282 284	640723201830
SPT(16)	2338443939469874221	0 30 46 76 90 100 108 142 186 220 228 238 252 282 298 328	656005025534