Prime p₀= 2004404641052966291 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 40 2 34 2 28 2 22 2 46 2 (?)
a_n: 0 2 18 20 60 62 96 98 126 128 150 152 198 200
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: 200
Found by: Dingo
db: batch=80, k=14, 16 40 34 28 22 46

SPT(16)	2004401987302150427	0 32 36 62 66 80 84 104 222 242 246 260 264 290 294 326	-2653750815864
SPT(16)	2004403294260186871	0 22 28 72 78 100 112 130 168 186 198 220 226 270 276 298	-1346792779420
STPT(10)	2004403310931453329	0 2 42 44 60 62 78 80 120 122	-1330121512962
SPT(16)	2004403773310891489	0 60 64 84 108 130 150 154 228 232 252 274 298 318 322 382	-867742074802
STPT(12)	2004403789960819109	0 2 30 32 42 44 78 80 90 92 120 122	-851092147182
SPT(16)	2004403972341681707	0 20 84 104 110 140 192 200 216 224 276 306 312 332 396 416	-668711284584
SPT(16)	2004404826593930011	0 6 28 72 76 82 88 96 172 180 186 192 196 240 262 268	185540963720
SPT(16)	2004404973878951471	0 6 20 42 102 150 182 198 200 216 248 296 356 378 392 398	332825985180
STPT(10)	2004405262366590287	0 2 12 14 42 44 72 74 84 86	621313623996
SPT(16)	2004405266834332829	0 20 48 68 102 104 122 158 174 210 228 230 264 284 312 332	625781366538
TPT(14)	2004405360281690369	0 2 12 14 48 50 78 80 90 92 150 152 168 170	719228724078