Taking the modulus of 2 arrays [closed]

I'm putting together a primality tester for large numbers. When the numbers were smaller things were more straightforwards. I got refined it to a point where I could quickly test any number within the range of long long ints. I wanted to be able to test larger numbers. I've gotten it to read the numbers in as strings then convert to an array. I now have the issue of not knowing how to perform mod on arrays. (int*)mod(int) isn't too bad but (int*)mod(int*) is more complicated.

In short:

1. Is there a relationship between n%c and n%a,n%b where a+b=c

2. How do you take the mod of 2 sums where either sum would give you overload.

• The description part of your question is pure implementation problem, which is not clearly stated and off-topic here. We prefer to state one question per post and also to make some research prior to asking. 1) looks like pure math, 2) part is unclear - how do you store the number if it causes overload? If this is causing all the trouble, it is unfortunatelly off-topic here because it asks about implementation details (might be on-topic on Stack Overflow). – Evil May 22 '16 at 22:28
• Sounds like an XY problem. See en.wikipedia.org/wiki/Primality_test. – D.W. May 22 '16 at 22:47

There is no useful relationship between $n \bmod (a+b)$ and $n \bmod a$ and $n \bmod b$. I don't see where this would come up anyway. (On the other hand, $(a+b) \bmod p$ is either $(a \bmod p) + (b \bmod p)$ or $(a \bmod p) + (b \bmod p) - p$ depending on whether the sum overflows $p$).
When computing with numbers modulo $n$, always reduce modulo $n$ after each operation, to avoid having numbers grow too large. During one operation, it's usually useful to allow one more digit, to accumulate carries on partial results.