Prime p₀= 2004125361653576807 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 238 2 28 2 82 2 28 2 28 2 34 2 (?)
a_n: 0 2 240 242 270 272 354 356 384 386 414 416 450 452
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: 452
Found by: MarkRBright
db: batch=80, k=14, 238 28 82 28 28 34

STPT(10)	2004123936429922631	0 2 36 38 78 80 120 122 156 158	-1425223654176
SPT(16)	2004124562324657419	0 22 52 78 108 192 264 304 318 358 430 514 544 570 600 622	-799328919388
SPT(16)	2004124720467634301	0 6 20 78 80 108 150 158 168 176 218 246 248 306 320 326	-641185942506
SPT(16)	2004124728367748663	0 14 18 54 68 80 98 108 110 120 138 150 164 200 204 218	-633285828144
SPT(16)	2004124925477745137	0 26 56 72 84 92 110 132 134 156 174 182 194 210 240 266	-436175831670
SPT(16)	2004124992326717023	0 30 36 40 54 66 70 124 210 264 268 280 294 298 304 334	-369326859784
TPT(16)	2004125499856533797	0 2 30 32 84 86 132 134 204 206 330 332 342 344 384 386	138202956990
SPT(16)	2004125510797725577	0 12 42 94 124 142 150 160 174 184 192 210 240 292 322 334	149144148770
STPT(10)	2004125524171308269	0 2 42 44 90 92 138 140 180 182	162517731462
TPT(14)	2004125837282497781	0 2 30 32 66 68 108 110 156 158 228 230 240 242	475628920974
SPT(16)	2004125857195421327	0 2 14 26 44 60 92 146 210 264 296 312 330 342 354 356	495541844520