Prime p₀= 2361685543669733159 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 160 2 58 2 64 2 28 2 58 2 (?)
a_n: 0 2 60 62 222 224 282 284 348 350 378 380 438 440
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: 440
Found by: Landjunge
db: batch=81, k=14, 58 160 58 64 28 58

TPT(14)	2361683279281050677	0 2 12 14 30 32 84 86 234 236 252 254 264 266	-2264388682482
TPT(14)	2361683328814351877	0 2 252 254 324 326 360 362 390 392 420 422 474 476	-2214855381282
TPT(14)	2361683424878135051	0 2 36 38 108 110 210 212 306 308 336 338 390 392	-2118791598108
SPT(16)	2361684228069332473	0 4 90 118 154 180 198 240 268 310 328 354 390 418 504 508	-1315600400686
SPT(16)	2361685145314660939	0 34 60 64 132 144 210 222 400 412 478 490 558 562 588 622	-398355072220
STPT(10)	2361685403153685491	0 2 36 38 78 80 120 122 156 158	-140516047668
STPT(10)	2361686222597874791	0 2 90 92 108 110 126 128 216 218	678928141632
SPT(16)	2361686301073554523	0 18 60 84 118 154 190 220 228 258 294 330 364 388 430 448	757403821364
STPT(10)	2361686850742934381	0 2 6 8 18 20 30 32 36 38	1307073201222
SPT(16)	2361687258179530273	0 10 16 18 66 76 124 174 220 270 318 328 376 378 384 394	1714509797114
TPT(14)	2361687392167822727	0 2 30 32 84 86 114 116 150 152 180 182 192 194	1848498089568