Is it true that every even number n ≥ 12 can be written as the sum of two
different primes plus a multiple of 4 (i. e. for all n ≥ 12, n = p + q + 4k, where p and q are
primes, p does not equal q, and k ∈ N ∪ {0})? If so, prove it, if not, provide a counterexample.

Question

Is it true that every even number n ≥ 12 can be written as the sum of two
different primes plus a multiple of 4 (i. e. for all n ≥ 12, n = p + q + 4k, where p and q are
primes, p does not equal q, and k ∈ N ∪ {0})? If so, prove it, if not, provide a counterexample.

anonymous · Answer

yes its true

anonymous · Answer

even numbers can be written as 4m or 4m+2 right ?

anonymous · Answer

yes

anonymous · Answer

4m=3+5+4(m-2)

anonymous · Answer

can u find a similar thing for 4m+2 ???

anonymous · Answer

I dont understand why you have 4(m-2) what is m-2? Can you please explain

anonymous · Answer

k is a arbitrary number right ?

anonymous · Answer

yes

anonymous · Answer

so when i want to write 4m in the form p+q+4k i choose k=m-2

anonymous · Answer

let suppose u have n=16=4*4  so m=4 i choose k=m-2=2 so 

16=3+5+4*2

anonymous · Answer

oh i see thank you

anonymous · Answer

what about the other one?