Prime p₀= 2356074094811257151 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 64 2 118 2 118 2 52 2 34 2 (?)
a_n: 0 2 60 62 126 128 246 248 366 368 420 422 456 458
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: 458
Found by: [AF] Kalianthys
db: batch=81, k=14, 58 64 118 118 52 34

SPT(16)	2356072700656673773	0 66 78 106 228 250 256 298 378 420 426 448 570 598 610 676	-1394154583378
TPT(14)	2356072709724312407	0 2 12 14 330 332 372 374 384 386 420 422 462 464	-1385086944744
SPT(16)	2356072769049190531	0 18 40 42 90 118 142 162 208 228 252 280 328 330 352 370	-1325762066620
SPT(16)	2356073055519489991	0 42 60 70 138 156 168 226 252 310 322 340 408 418 436 478	-1039291767160
STPT(10)	2356073458968879701	0 2 6 8 18 20 30 32 36 38	-635842377450
STPT(10)	2356073961655890599	0 2 12 14 30 32 48 50 60 62	-133155366552
SPT(16)	2356074113289845363	0 18 24 60 86 120 126 134 150 158 164 198 224 260 266 284	18478588212
STPT(10)	2356074244241256137	0 2 30 32 42 44 54 56 84 86	149429998986
SPT(16)	2356074576430670983	0 24 28 30 40 88 94 108 130 144 150 198 208 210 214 238	481619413832
STPT(10)	2356074806932903487	0 2 54 56 72 74 90 92 144 146	712121646336
TPT(14)	2356074906406982777	0 2 30 32 120 122 144 146 162 164 210 212 240 242	811595725626