Prime p₀= 2097551994215474831 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 4 2 58 2 10 2 10 2 4 2 (?)
a_n: 0 2 60 62 66 68 126 128 138 140 150 152 156 158
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: 158
Found by: [SG-2W]Kurzer
db: batch=80, k=14, 58 4 58 10 10 4

SPT(16)	2097550585607840393	0 8 20 24 38 84 90 114 134 158 164 210 224 228 240 248	-1408607634438
SPT(16)	2097550602911295557	0 2 86 102 104 126 156 174 182 200 230 252 254 270 354 356	-1391304179274
TPT(14)	2097550816842949667	0 2 24 26 90 92 174 176 192 194 342 344 414 416	-1177372525164
STPT(10)	2097551117670899489	0 2 18 20 30 32 42 44 60 62	-876544575342
TPT(14)	2097551143941384797	0 2 30 32 54 56 150 152 162 164 180 182 204 206	-850274090034
SPT(16)	2097551670865690063	0 6 10 36 66 78 120 136 150 166 208 220 250 276 280 286	-323349784768
STPT(10)	2097552299699713397	0 2 30 32 72 74 114 116 144 146	305484238566
TPT(14)	2097552671492472281	0 2 48 50 90 92 150 152 216 218 258 260 390 392	677276997450
SPT(16)	2097552852446774873	0 68 128 170 174 198 204 216 218 230 236 260 264 306 366 434	858231300042
SPT(16)	2097552990439005139	0 34 42 102 148 160 172 178 204 210 222 234 280 340 348 382	996223530308
SPT(16)	2097553329393804839	0 8 14 18 72 84 90 120 152 182 188 200 254 258 264 272	1335178330008