Prime p₀= 2004393565247188571 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 28 2 40 2 4 2 40 2 286 2 (?)
a_n: 0 2 78 80 108 110 150 152 156 158 198 200 486 488
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: 488
Found by: Dingo
db: batch=80, k=14, 76 28 40 4 40 286

SPT(16)	2004392379843213337	0 24 82 106 150 186 204 214 252 262 280 316 360 384 442 466	-1185403975234
SPT(16)	2004392592364315397	0 2 32 54 66 74 84 116 150 182 192 200 212 234 264 266	-972882873174
TPT(14)	2004392652090938531	0 2 156 158 186 188 246 248 270 272 288 290 366 368	-913156250040
STPT(10)	2004392705576931581	0 2 6 8 18 20 30 32 36 38	-859670256990
SPT(16)	2004392804871810487	0 4 36 40 54 70 72 102 124 154 156 172 186 190 222 226	-760375378084
STPT(10)	2004393305770037849	0 2 18 20 30 32 42 44 60 62	-259477150722
SPT(13)	2004393652660136809	0 30 54 180 192 240 252 264 312 324 450 474 504	87412948238
SPT(16)	2004393992279326321	0 10 42 46 58 72 102 156 172 226 256 270 282 286 318 328	427032137750
SPT(16)	2004394712670526661	0 30 38 42 140 168 198 200 210 212 242 270 368 372 380 410	1147423338090
TPT(14)	2004395084897218721	0 2 30 32 78 80 138 140 168 170 276 278 360 362	1519650030150
STPT(10)	2004395404828398467	0 2 30 32 42 44 54 56 84 86	1839581209896