Prime p₀= 2623687705133636567 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 34 2 22 2 184 2 10 2 28 2 (?)
a_n: 0 2 24 26 60 62 84 86 270 272 282 284 312 314
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: 314
Found by: JayPi
db: batch=82, k=14, 22 34 22 184 10 28

STPT(10)	2623686616378976381	0 2 30 32 78 80 126 128 156 158	-1088754660186
SPT(16)	2623686828044353427	0 26 72 90 156 192 210 222 224 236 254 290 356 374 420 446	-877089283140
SPT(16)	2623687123322122133	0 20 30 44 128 168 194 210 224 240 266 306 390 404 414 434	-581811514434
STPT(10)	2623687136291554547	0 2 30 32 42 44 54 56 84 86	-568842082020
SPT(16)	2623687317147777007	0 40 46 66 102 166 180 186 190 196 210 274 310 330 336 376	-387985859560
TPT(16)	2623687452299482769	0 2 12 14 102 104 180 182 258 260 390 392 420 422 558 560	-252834153798
TPT(14)	2623687979956210499	0 2 90 92 138 140 192 194 252 254 288 290 300 302	274822573932
SPT(16)	2623688091074700547	0 16 36 76 106 126 144 156 160 172 190 210 240 280 300 316	385941063980
SPT(16)	2623688456512562111	0 8 30 78 92 96 138 168 170 200 242 246 260 308 330 338	751378925544
SPT(16)	2623688689188583543	0 4 36 94 108 174 178 184 330 336 340 406 420 478 510 514	984054946976
SPT(16)	2623688913192064829	0 48 74 80 102 140 174 234 248 308 342 380 402 408 434 482	1208058428262