Is it true that all primes above 5 have a remainder of either

How the fuck should I know?

>>7975987

code and test it faggot

>>7975987
I think so.
Let's check.
Rem = 0: Div by 6, not prime.
Rem = 1: Well, 13 is prime.
Rem =2: Then since 2 div 6 and 2 div 2, not prime.
Rem =3: Then since 3 div 6 and 3 div 3, not prine.
Rem = 4: Then since 2 div 6 and 2 div 4, not prime.
Rem = 5: Well, 17 is prime.

So, yes.

>>7975987
Jesus OP you're fucking dumb. You should drop whatever class this is homework for as soon as you can.

The answer is yes.

Remainders:
0- divisible by 6, obviously not prime
1- maybe prime
2- divisible by 2, obviously not prime
3- divisible by 3, obviously not prime
4- divisible by 4, obviously not prime
5- maybe prime

>>7976767
In fact, we can generalize this:
Let p be a prime and let n be a number less than p. Then the remainder of p divided by n is not divisible by any nontrivial factors of n.

>>7976758
Do you always jump straight to computer simulations when it would take less time to check by hand? There are only three cases to consider, and they only involve writing out a definition .

>>7976784

I'm just a lowly CS undergrad, consistently proving things without a compiler to tell me where I fucked up is beyond my puny skills, pls no bully ;_;

>>7976797
It's time to learn, anon. Sometimes your code could be buggy or it may take a long time to find counterexamples. You can do it.

>>7976774
>4- divisible by 4, obviously not prime

by 2 you mean

>>7976774
OP here.
Do you have mental retardation or something?
You've clearly shown that you failed to understand the problem.

And my question isn't homework - I posted it for general entertainment and to see how others would approach this simple problem (hence the smug pepe in the OP).
I know that my statement is true, since it follows from the definition of prime numbers.

thought about it for a few seconds, tried a few test cases, then came to the same conclusion as this smart mofo >>7976767
neat