Just found that seems any even number which greater than 2 can be decomposed into the XOR of two prime numbers.↵
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It can be proven when n <= 1e9(by code).↵
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Can anyone prove it or falsify it?↵
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Edit:↵
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It seems that every even integer $n$ (in any base $k$) can be represented as the digit-wise sum of two primes without carry.↵
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Moreover, ↵
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for every odd integer $n$ (in an odd base $k$) can be represented as the digit-wise sum of two primes without carry.↵
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Are they right?
↵
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?
