/sci/ - Science & Math

it can be expressed as the sum of a prime and co-prime.

No, but every number greater than 3 can.

>>3576361

> 5 = 3 + 3
I do believe 3 is not co-prime to 3.

>>3576382
Not every number, every even number.

http://www.youtube.com/watch?v=PtsrAw1LR3E

i don't remember if it is mentioned in this video but you surely want to give it a look

no. good luck to do it with 37. (impossible since if you take two odd prime numbers, they'll add up to an even number, so one of the two prime numbers must be 2. And 35 will be the other. 35 isn't prime.)
/thread?

>>3576399
Of fuck what a fail

> 6 = 3 + 3

assume you cant
then there exists 2 numbers k and g such that one cant be written as p + n with n and p prime
kg = (p+n)(m+q) = pm + pq + nm + nq all prime
these are 2 new numbers i = (pm + pq) and j = (nm + nq) both sums of co-primes
unless k and g are both prime, kg can always be written as ij = (pm + pq)(nm + nq)
now kg = (pm + pq)(nm + nq)
but kg = (p+n)(m+q)
and (pm + pq)(nm + nq) =/= (p+n)(m+q)
so our initial assumption is incorrect and you can.

>>3576405
37 is prime. Derp.

>>3576424
so? it's not a sum of two primes.

>>3576405
>37
>even
>2011

>>3576347
Holy shit, 10 billion people have trouble with fractions...?

That's a LOT more than I thought...

>>3576426
Wtf? lol I think you just proved Goldbach's conjecture false.

>>3576458
Wait no. 37 is not even.

>>3576462
yes, OP might have mixed "any number" with "any even number" ;)

hahaha this definitely *isn't* a famous unproven conjecture/open problem

>every even integer greater then 2
>solved it! 37

The fuck?

>>3576485
37 isn't even.

>>3576479
>Can every even number greater than 2
>Can every even number
>even number

b = 2m {m| 2 ≤ m < ∞, b ∈ ℤ}
b = a + c where a and c are prime. There is no known formula for the sequence of prime numbers. However, we can make some observations. The sum of any two primes is even unless only one is 2. As b increases, the value and number of digits of the primes gradually increase. The difference of two primes sequentially adjacent is relatively small even up to primes just below 1000. This means that we have a rather robust collection of numbers to create an even integer out of two of them. I can only make the educated guess that all even integers is the sum of two primes. It pretty much impossible to prove without a function for the set of prime numbers.

5740
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#include <cstdlib>
#include <iostream>

using namespace std;

int main(){
double c(2);
while(true){
bool prime(true);
for(size_t i=2;i<(c/2)+1;i++){
if(c/double(i)==int(c/double(i))){
prime=false;
}
}
if(prime){
cout<<c<<endl;
}
c++;
}
return 0;
}
./a.out >prime