A mathematical curio

enzocreti · 2018-11-26, 12:17

6*210^4-210+210^2=2 · 3 · 5 · 7 · 7351 · 7559
6*210^4-210-210^2=2*3*5*7*7349*7561!!!

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

axn · 2018-11-26, 13:20

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)

2018-11-26, 12:17	#1
enzocreti Mar 2018 2×5×53 Posts	A mathematical curio 6210^4-210+210^2=2 · 3 · 5 · 7 · 7351 · 7559 6210^4-210-210^2=23577349*7561!!! where 7351-7349 and 7559-7561 are two pairs of twin prime!

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2018-11-26, 13:20	#2
axn Jun 2003 2²·3·421 Posts	we can get rid of the common factor 210. so the expressions simplify to: (6210^3-1)+210=73517559 (6210^3-1)-210=73497561 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)