Question 558730
<pre>
The square numbers it could be 1 more than are

                        9,16,25,36,49,64,81,100,121,144

Add 1 to each:         10,17,26,37,50,65,82,101,122,145

The only primes in that list are 17, 37, and 101, so it's one of those three.

The sums of digits of those are   8, 10, and   2

10 is the only sum of digits which is a multiple of 5.

So the answer is 37.

Edwin</pre>