Question

Number Theory.
Deduce whether :
5^ (12) + 2^(10) is prime or not.

Answer 1

2^10 =1024, easy to figure out
5^12 is going to end in a 0 or 5
hmm...
if it ends in a 5 your last digit is going to be seven...

Answer 2

doesn't help much as 19 is prime and 39 is not

Answer 3

so your looking at xxx...xxx(24+25)

Answer 4

14657×16657 (2 distinct prime factors) = 244141649

Anybody want to check my arithmetic?

Answer 5

nope I trust wolfram...

Answer 6

wolfam will factor in to the product of two primes, but i am fairly sure that is not the point of the problem

Answer 7

In short, no, it's not a prime # if it has factors.

Answer 8

yes... but how do you figure that out...

Answer 9

Prime factorization is what I used

Answer 10

an even power of 5 will always end in 625 (if power is greater than 2, obviously) if it's any help

Answer 11

5*5*5*5*5*5*5*5*5*5*5*5*2*2*2*2*2*2*2*2*2*2 (hopefully I counted right)

Answer 12

I don't know if this theory is correct by somebody told me a long time ago that even powers of base 2 never result in prime #'s

Answer 13

*

Answer 14

but somebody* ack typos

Answer 15

Anybody willing to disprove that theory? :D

Answer 16

any power of anything will never be prime, unless prime doesn't mean what I think it means?

Answer 17

5*5*5*5*5*5*5*5*5*5*5*5+2*2*2*2*2*2*2*2*2*2

Answer 18

/facepalm and I made another typo it seems:

Yeah this is what I should have typed...
5*5*5*5*5*5*5*5*5*5*5*5+2*2*2*2*2*2*2*2*2*2

Answer 19

I agree with @m_charron2

Answer 20

yes any power of anything will not be prime but the problem is that there adding two powers...
for example

2^2+3^2=13
see..

Answer 21

Hmm, time to go back to the definitions then eh?
http://en.wikipedia.org/wiki/Prime_number
^_^ (reading myself at the moment)

Answer 22

but by the same token: 7^2+2^2 =16
so the question becomes do they make a prime or not

Answer 23

7^2+2^2 = 53?

Answer 24

oh derp.. math fail!, how about this the 7^1 +3^1 =10, there..

Answer 25

Ah here we go, but I'll be honest and say that this is beyond my area of knowledge:
http://en.wikipedia.org/wiki/AKS_primality_test

Maybe somebody here could explain this? o_O

Answer 26

Polynomial based primes

Answer 27

yeah.. IDK

Answer 28

@myininaya number theory help?

Answer 29

@TuringTest Can you please explain the AKS_primality_test in layman's terms? I think that's probably the optimal answer to this question or any related to it that are sums of products (treating the variables of the polynomial as the product part)

Answer 30

I wish I could, but that's why I tagged myininaya; I don't know number theory very well
more possible helpers:
@asnaseer @FoolForMath number theory help anyone?

Answer 31

Guyssssss.
It's a really basic solution. Just factorize it :P.