Prime p₀= 1012111304521265327 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 70 2 124 2 22 2 94 2 40 2 (?)
a_n: 0 2 12 14 84 86 210 212 234 236 330 332 372 374
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: Theadalus
db: batch=76, k=14, 10 70 124 22 94 40

STPT(10)	1012110345456740729	0 2 42 44 90 92 138 140 180 182	-959064524598
SPT(16)	1012110406949873083	0 10 34 46 66 130 184 196 198 210 264 328 348 360 384 394	-897571392244
STPT(10)	1012110515846470277	0 2 30 32 42 44 54 56 84 86	-788674795050
SPT(16)	1012110757411526011	0 12 18 40 42 46 82 108 130 156 192 196 198 220 226 238	-547109739316
SPT(16)	1012110955228491121	0 16 82 106 148 196 216 222 346 352 372 420 462 486 552 568	-349292774206
STPT(10)	1012110981431743967	0 2 54 56 72 74 90 92 144 146	-323089521360
SPT(16)	1012111345904527933	0 10 30 36 64 100 114 124 126 136 150 186 214 220 240 250	41383262606
TPT(14)	1012111355838204077	0 2 42 44 54 56 84 86 150 152 210 212 222 224	51316938750
STPT(12)	1012111860951180959	0 2 12 14 30 32 72 74 90 92 102 104	556429915632
SPT(16)	1012112067853686361	0 22 42 78 90 106 108 132 136 160 162 178 190 226 246 268	763332421034
STPT(10)	1012112516077465487	0 2 24 26 42 44 60 62 84 86	1211556200160