Prime p₀= 2004254646419275949 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 178 2 28 2 16 2 10 2 28 2 136 2 (?)
a_n: 0 2 180 182 210 212 228 230 240 242 270 272 408 410
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: 410
Found by: Dingo
db: batch=80, k=14, 178 28 16 10 28 136

SPT(16)	2004252662795059879	0 54 88 90 108 124 168 174 178 184 228 244 262 264 298 352	-1983624216070
SPT(16)	2004253753470096157	0 16 82 96 100 124 154 184 222 252 282 306 310 324 390 406	-892949179792
TPT(14)	2004254001134825681	0 2 36 38 96 98 126 128 150 152 258 260 348 350	-645284450268
STPT(10)	2004254007076657277	0 2 30 32 42 44 54 56 84 86	-639342618672
STPT(10)	2004254058316175681	0 2 36 38 78 80 120 122 156 158	-588103100268
SPT(16)	2004254239250494817	0 14 24 84 126 150 164 186 200 222 236 260 302 362 372 386	-407168781132
STPT(10)	2004254809796379599	0 2 18 20 30 32 42 44 60 62	163377103650
SPT(16)	2004255064424535253	0 6 16 34 60 108 144 148 156 160 196 244 270 288 298 304	418005259304
SPT(16)	2004255424587462637	0 12 42 66 82 96 106 120 142 156 166 180 196 220 250 262	778168186688
SPT(16)	2004255435191394677	0 12 26 42 62 84 120 140 186 206 242 264 284 300 314 326	788772118728
STPT(10)	2004255488019772187	0 2 30 32 72 74 114 116 144 146	841600496238