Just found that seems any even number which greater than 2 can be decomposed into the XOR of two prime numbers.

It can be proven when n <= 1e9(by code).

Can anyone prove it or falsify it?

Edit:

It seems that every even integer $$$n$$$ (in any base $$$k$$$) can be represented as the digit-wise sum of two primes without carry.

Moreover,

for every odd integer $$$n$$$ (in an odd base $$$k$$$) can be represented as the digit-wise sum of two primes without carry.

Are they right?