A mathematical curio
 

6*210^4-210+210^2=[URL="https://factordb.com/index.php?id=2"][COLOR=#000000]2[/COLOR][/URL] · [URL="https://factordb.com/index.php?id=3"][COLOR=#000000]3[/COLOR][/URL] · [URL="https://factordb.com/index.php?id=5"][COLOR=#000000]5[/COLOR][/URL] · [URL="https://factordb.com/index.php?id=7"][COLOR=#000000]7[/COLOR][/URL] · [URL="https://factordb.com/index.php?id=7351"][COLOR=#000000]7351[/COLOR][/URL] · [URL="https://factordb.com/index.php?id=7559"][COLOR=#000000]7559[/COLOR][/URL]
6*210^4-210-210^2=2*3*5*7*7349*7561!!!


where 7351-7349 and 7559-7561 are two pairs of twin prime!

we can get rid of the common factor 210. so the expressions simplify to:

(6*210^3-1)+210=7351*7559
(6*210^3-1)-210=7349*7561

Now, consider the pair of numbers (x, x+2), (x+d, x+d+2).
(x+2)*(x+d)-x*(x+d+2) = 2*d

here d=210 (7559-7349=7561-7351)