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Most non-negative integers can be written as the sum of a prime number plus a perfect square. For instance, 21 can be written as What is the smallest number greater than 1 which cannot be expressed in this way?

 Oct 1, 2019
 #1
avatar+104962 
+3

2 can be written  as  2 (a prime)  + 0  (a perfect square)

3 can be written as  2 ( a prime) + 1  (a perfect square)

4  can be written as  3 (prime) + 1 (a perfect square)

5 =   5 (a prime)  + 0 (a perfect square)

6  =   5 (prime) + 1 (a perfect square)

7 = 3 (prime) + 4 (a perfect square)

8 =   7 (prime) + 1 (perfect square)

9 = 5 (prime) + 4 (perfect square)

 

10

0 (perfect square) + 10 (non-prime)  

1 + 9    sum of two squares

2 (prime) + 8 (non-square)

3 + 7 sum of two primes

4 (perfect square) + 6 (non-prime)

5 + 5  sum of two primes

 

 

cool cool cool

 Oct 1, 2019
 #2
avatar+33 
+2

Thanks, I understand my mistake. I didnt consider 0 to be a perfect square

 Oct 1, 2019

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