A Late Night ConversationComputer Science Level 5
She: Why aren't you replying for last two minutes?
Me: My computer just stopped responding.
She: Isn't that just an excuse to not talk to me?
Me: No, dear. I just calculated that <LargePrimeX> + <LargePrimeY> = <YourPhoneNumber> where <LargePrimeX> and <LargePrimeY> are prime numbers.
She: You do all these up so late?
She: Had it been any other girl, she'd have gone mad. Only because it's me, I've been in sound mental health for so long!
I recently realised that the last four digits of her phone number can be expressed as a sum of two primes in 103 ways.
What is the maximum possible value of the last four digits of her phone number?
Details and Assumptions:
PrimeA + PrimeB and PrimeB + PrimeA are counted as the same solution.
The primes need not be distinct.
22 can be written as a sum of two primes in three ways.