how to prove that 222221 is not a prime number?

Question

anonymous · Answer

write it as 19*116959

nowhereman · Answer

No, 19*116959 = 2.222.221 but he is talking about 222.221

nowhereman · Answer

But it is 359*619

dumbcow · Answer

i dont know
write a program and try dividing it by every prime number before it :)

nowhereman · Answer

That's just what I did :-)
No idea how you can prove it more easily :-D

anonymous · Answer

nice one dumbcow...
hey satalite , u got 22,22,22 1 
see question , 22,22,2 1 :(

anonymous · Answer

hey nowhereman, how did u get these factors?

anonymous · Answer

oops sorry. i read it wrong. then outside of testing all primes up until 471 i don't see a snap way of doing it. that is why codes are based on factoring. it takes a long time

nowhereman · Answer

Just by trying all from 1 to $\sqrt{222,221}$ with a short python script.

anonymous · Answer

only till root of that number?

nowhereman · Answer

yeah that's enough. But there is still a better way:
Just use Fermat's small theorem. You'll see that 222221 can't be a prime number because $$2^{222220} = 72600 \neq  1 \mod 222221$$