Prime p₀= 2789788675309439159 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 76 2 58 2 28 2 22 2 4 2 (?)
a_n: 0 2 30 32 108 110 168 170 198 200 222 224 228 230
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: 230
Found by: matsu_pl
db: batch=82, k=14, 28 76 58 28 22 4

SPT(16)	2789786743775430353	0 8 54 66 120 146 164 170 174 180 198 224 278 290 336 344	-1931534008806
STPT(10)	2789786841785494937	0 2 12 14 42 44 72 74 84 86	-1833523944222
SPT(16)	2789787092980637369	0 2 68 72 90 114 120 132 140 152 158 182 200 204 270 272	-1582328801790
STPT(10)	2789787565584819467	0 2 90 92 132 134 174 176 264 266	-1109724619692
SPT(16)	2789788420878603541	0 70 102 126 232 246 262 276 316 330 346 360 466 490 522 592	-254430835618
SPT(16)	2789788595789159191	0 12 30 52 66 96 100 106 156 162 166 196 210 232 250 262	-79520279968
SPT(16)	2789788789611525077	0 12 24 96 126 134 180 192 194 206 252 260 290 362 374 386	114302085918
STPT(12)	2789788806641101961	0 2 36 38 48 50 78 80 90 92 126 128	131331662802
STPT(10)	2789788811551591061	0 2 36 38 78 80 120 122 156 158	136242151902
SPT(16)	2789788827792547433	0 6 20 30 48 56 90 140 156 206 240 248 266 276 290 296	152483108274
SPT(16)	2789789066568892939	0 12 52 78 124 144 154 162 220 228 238 258 304 330 370 382	391259453780