As I was reading my number theory textbook I came across the following question after reading about the idea of infinitely many primes:
There is only one prime number that can be written both as the sum of two primes and the difference of two primes. Find that number and prove that it is the only one.
I’ve been thinking it could be 5? Since $2+3=5$ and $7-2=5$. However, I’m not sure.
As far as proving that number is the only one: should I reference Goldbach’s Conjecture or something along those lines? Any hints would be greatly appreciated.