Prime p₀= 2820462352226220461 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 34 2 40 2 46 2 40 2 10 2 (?)
a_n: 0 2 90 92 126 128 168 170 216 218 258 260 270 272
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: 272
Found by: JayPi
db: batch=82, k=14, 88 34 40 46 40 10

SPT(16)	2820459432292214023	0 36 150 174 216 220 276 304 306 334 390 394 436 460 574 610	-2919934006438
STPT(10)	2820460207011492581	0 2 6 8 48 50 90 92 96 98	-2145214727880
SPT(16)	2820460354905340681	0 18 36 48 76 102 130 156 202 228 256 282 310 322 340 358	-1997320879780
STPT(10)	2820460359815065787	0 2 30 32 42 44 54 56 84 86	-1992411154674
SPT(16)	2820461964314624257	0 4 70 84 90 94 102 132 172 202 210 214 220 234 300 304	-387911596204
STPT(10)	2820462112008464969	0 2 42 44 90 92 138 140 180 182	-240217755492
STPT(10)	2820462562417191017	0 2 30 32 42 44 54 56 84 86	210190970556
SPT(16)	2820462579772250173	0 96 144 190 256 258 270 304 330 364 376 378 444 490 538 634	227546029712
SPT(16)	2820462606428180017	0 10 40 54 66 76 90 100 150 160 174 184 196 210 240 250	254201959556
SPT(16)	2820462734807860817	0 2 54 72 80 96 140 182 204 246 290 306 314 332 384 386	382581640356
SPT(16)	2820463057446910241	0 6 18 66 90 92 126 150 158 182 216 218 242 290 302 308	705220689780