Prime p₀= 2066210650592016491 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 10 2 100 2 64 2 52 2 196 2 (?)
a_n: 0 2 66 68 78 80 180 182 246 248 300 302 498 500
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: Cruncher Pete
db: batch=80, k=14, 64 10 100 64 52 196

SPT(16)	2066208206994443221	0 10 30 76 118 120 136 156 202 222 238 240 282 328 348 358	-2443597573270
SPT(13)	2066208286096788887	0 36 42 102 120 180 216 252 312 330 390 396 432	-2364495227604
SPT(16)	2066208509371982333	0 24 66 68 114 116 140 150 254 264 288 290 336 338 380 404	-2141220034158
SPT(16)	2066208539773174463	0 24 78 86 90 116 156 186 188 218 258 284 288 296 350 374	-2110818842028
STPT(10)	2066209319059832699	0 2 18 20 30 32 42 44 60 62	-1331532183792
SPT(16)	2066210284357738061	0 26 60 92 116 170 210 240 242 272 312 366 390 422 456 482	-366234278430
STPT(10)	2066210820832601921	0 2 30 32 78 80 126 128 156 158	170240585430
SPT(18)	2066211510855344953	0 60 66 136 156 184 190 216 244 270 298 324 330 358 378 448 454 514	860263328462
SPT(16)	2066211728762879681	0 2 32 42 78 98 126 188 210 272 300 320 356 366 396 398	1078170863190
SPT(16)	2066211868772056009	0 82 90 114 132 154 160 180 202 222 228 250 268 292 300 382	1218180039518
SPT(16)	2066211930200151911	0 2 6 48 72 78 86 92 126 132 140 146 170 212 216 218	1279608135420