Prime p₀= 2315723453380603919 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 28 2 28 2 94 2 100 2 88 2 (?)
a_n: 0 2 72 74 102 104 132 134 228 230 330 332 420 422
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: 422
Found by: Landjunge
db: batch=81, k=14, 70 28 28 94 100 88

TPT(14)	2315722231899497171	0 2 78 80 90 92 186 188 216 218 240 242 288 290	-1221481106748
TPT(14)	2315722272751137587	0 2 42 44 54 56 162 164 210 212 264 266 294 296	-1180629466332
STPT(10)	2315722754372440337	0 2 12 14 42 44 72 74 84 86	-699008163582
SPT(16)	2315722852763674691	0 80 108 110 140 150 206 218 228 240 296 306 336 338 366 446	-600616929228
SPT(16)	2315722984817690153	0 24 38 104 110 114 138 140 198 200 224 228 234 300 314 338	-468562913766
STPT(10)	2315723408803327709	0 2 42 44 90 92 138 140 180 182	-44577276210
SPT(16)	2315723800668086891	0 18 38 42 62 68 108 110 300 302 342 348 368 372 392 410	347287482972
SPT(16)	2315724438439517269	0 30 58 72 82 94 150 222 250 322 378 390 400 414 442 472	985058913350
STPT(10)	2315724513137282519	0 2 18 20 30 32 42 44 60 62	1059756678600
SPT(16)	2315724723274544081	0 26 42 90 96 110 146 152 156 162 198 212 218 266 282 308	1269893940162
TPT(14)	2315724743895667787	0 2 12 14 42 44 60 62 90 92 114 116 144 146	1290515063868