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it has adkdgbsgbsd'g SD
Start at 1. That is a Square. Add 3 to make 4 (another square) . Keep on adding successive odd numbers, and each time you will have another square. To understand this think of 9 dots arranged in 3 rows ( a 3 x 3 square). To make the next square you have to add n dots along the top, n dots down the side, and 1 extra in the corner. Thats 2n+1 dots. You originally had n2 . Now you have (n+1)2 simply by adding the odd number 2n+1. Recall that (n+1)2 = n2+2n+1. This is the basis for an old method for finding square roots.
I can't give a good way to remember prime numbers based on their name, but for square numbers, you can just remember it as a figure: You can think of numbers as a collection of dots, so 1 = * 2 = * * 3 = * * * etc. Now, if you form a square with n dots on the side, the number of dots in the square will be n^2. This is why they are called "square numbers". For instance: 1^2 = 1 * 2^2 = 4 * * * * 3^2 = 9 * * * * * * * * * etc. So the number n^2 is the number of dots in the square with n dots on each side. The ancient Greeks were into this kind of representation of numbers and devoted much study to what are called "figurate numbers", meaning "numbers that can be represented by a figure". In particular, they looked at triangular numbers, rectangular numbers, and pentagonal numbers, in addition to what I just showed you with square numbers. Getting back to your original question, remember square numbers as the number of dots in a *square* of dots. As for primes, if you are having issues with only primes and squares, just remember it as "not square numbers".
You would be 5 years old
If n is one integer, then the consecutive integer to it is n+1, and the next is n+2 and so on.