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How many perfect squares are 1 more than a prime?

 Jun 25, 2020
 #1
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Sorry, I got it backwards !! Thanks EP.

 Jun 25, 2020
edited by Guest  Jun 25, 2020
edited by Guest  Jun 25, 2020
 #2
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4   is ONE    ( counting up to 1024)   maybe the ONLY one?

 Jun 25, 2020
 #3
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all primes (except 2--but 3 is obviously not a perfect square) are odd. That means the perfect square must be even. And as EP has said 4 is one of them and I also don't know if there are any other options.

 Jun 25, 2020
 #4
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How many perfect squares are 1 more than a prime?  

 

Brute Force.  I tried all of them from 12 to 1002 inclusive.  4 is the only one I found.  Actually, I didn't try all of them.  It isn't necessary to try numbers whose square ends in a 1, 5, 6, or 9. 

.

 Jun 26, 2020

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