Prime p₀= 976020733075471859 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 178 2 88 2 34 2 28 2 28 2 (?)
a_n: 0 2 42 44 222 224 312 314 348 350 378 380 408 410
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: Theadalus
db: batch=76, k=14, 40 178 88 34 28 28

SPT(16)	976019822807094629	0 2 72 102 120 158 182 200 282 300 324 362 380 410 480 482	-910268377230
SPT(16)	976019854380185093	0 6 84 86 108 164 188 198 266 276 300 356 378 380 458 464	-878695286766
SPT(16)	976020227130039449	0 8 42 72 128 144 164 180 182 198 218 234 290 320 354 362	-505945432410
STPT(10)	976020312408647711	0 2 6 8 18 20 30 32 36 38	-420666824148
TPT(14)	976020516251531141	0 2 108 110 156 158 180 182 186 188 276 278 306 308	-216823940718
SPT(13)	976020567942109889	0 24 90 138 150 168 174 180 198 210 258 324 348	-165133361970
STPT(10)	976020992292897149	0 2 18 20 30 32 42 44 60 62	259217425290
STPT(10)	976021144704892367	0 2 54 56 72 74 90 92 144 146	411629420508
SPT(16)	976021355846715319	0 4 18 42 52 70 82 88 144 150 162 180 190 214 228 232	622771243460
SPT(16)	976021638355101133	0 28 48 64 76 118 136 168 196 228 246 288 300 316 336 364	905279629274
STPT(12)	976021645646890691	0 2 30 32 78 80 120 122 168 170 198 200	912571418832