7 is a prime number and 7+1=8 is a perfect cube. Can you find another prime number p such that p+1 is a perfect cube?

- via Daily Brain Teaser

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7 is a prime number and 7+1=8 is a perfect cube. Can you find another prime number p such that p+1 is a perfect cube?

- via Daily Brain Teaser

No because x^3 - 1 = (x - 1)(x^2 + x + 1), which is clearly not prime if x > 2.

When x = 2 is the ONLy time you get a prime. i.e 7.

Assume the integer c cubed follows prime P then

Then c^3 -1 = P

But c^3 -1= (c-1)(c^2 + c + 1)

The right side is composite unless (c-1) = 1

(c-1) = 1 iff c=2

If c=2 then (c^2 + c + 1) can only =7

Wh do you correct/edit the reply that Lizard gave and not edit mine?

Grow up phd candidate.