Integers that can only be divisible by 1 and itself are called prime numbers 2, 3, 5, 7 ... On the contrary, they are 4, 6 and 8. ...

Solution: If 2n+1= k 2, 3n+1= m 2,

Then 5n+3 = 4 (2n+1)-(3n+1) = 4k 2-m 2 = (2k+m) (2k-m).

Because 5n+3 > (3n+1)+2 = m2+2 > 2m+1,

So 2k-m≠ 1 (otherwise 5n+3 = 2k+m = 2m+ 1).

So 5n+3=(2k+m)(2k-m) is a composite number.