Prime p₀= 2821421171015900771 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 10 2 58 2 250 2 28 2 28 2 (?)
a_n: 0 2 36 38 48 50 108 110 360 362 390 392 420 422
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: 422
Found by: [SG-2W]Kurzer
db: batch=82, k=14, 34 10 58 250 28 28

SPT(16)	2821419163210461299	0 2 38 50 62 72 92 120 140 168 188 198 210 222 258 260	-2007805439472
SPT(16)	2821419314352474917	0 14 26 86 156 300 306 404 456 554 560 704 774 834 846 860	-1856663425854
SPT(16)	2821420027347662203	0 28 30 36 100 114 130 184 240 294 310 324 388 394 396 424	-1143668238568
SPT(16)	2821420561695565217	0 6 14 56 72 84 114 146 150 182 212 224 240 282 290 296	-609320335554
STPT(10)	2821420797614332337	0 2 54 56 72 74 90 92 144 146	-373401568434
STPT(10)	2821421079757952387	0 2 60 62 72 74 84 86 144 146	-91257948384
TPT(14)	2821421286600560849	0 2 18 20 60 62 78 80 168 170 210 212 228 230	115584660078
STPT(10)	2821421492290314437	0 2 30 32 42 44 54 56 84 86	321274413666
STPT(10)	2821421710828143749	0 2 18 20 30 32 42 44 60 62	539812242978
SPT(16)	2821421764014320653	0 6 70 84 96 130 138 154 300 316 324 358 370 384 448 454	592998419882
SPT(16)	2821421797125621499	0 12 18 60 94 108 160 162 220 222 274 288 322 364 370 382	626109720728