Prime p₀= 2350361063214946679 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 232 2 46 2 40 2 106 2 46 2 (?)
a_n: 0 2 18 20 252 254 300 302 342 344 450 452 498 500
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: 500
Found by: Landjunge
db: batch=81, k=14, 16 232 46 40 106 46

STPT(12)	2350359688679077937	0 2 12 14 24 26 30 32 42 44 54 56	-1374535868742
SPT(16)	2350360105135427641	0 76 90 102 120 132 142 172 240 270 280 292 310 322 336 412	-958079519038
STPT(10)	2350360157295085667	0 2 54 56 132 134 210 212 264 266	-905919861012
STPT(10)	2350360444182270857	0 2 30 32 120 122 210 212 240 242	-619032675822
SPT(16)	2350360665746587211	0 72 78 86 110 126 128 152 156 180 182 198 222 230 236 308	-397468359468
SPT(16)	2350360714813727503	0 4 6 16 40 66 90 150 160 220 244 270 294 304 306 310	-348401219176
SPT(16)	2350361265957841531	0 10 28 40 42 48 70 90 238 258 280 286 288 300 318 328	202742894852
SPT(16)	2350361582307208027	0 34 46 82 90 112 166 172 204 210 264 286 294 330 342 376	519092261348
STPT(10)	2350362288553888751	0 2 6 8 18 20 30 32 36 38	1225338942072
SPT(16)	2350362622225419719	0 12 24 38 68 80 120 152 210 242 282 294 324 338 350 362	1559010473040
SPT(16)	2350362826341277127	0 24 32 42 72 84 90 150 164 224 230 242 272 282 290 314	1763126330448