A Late Night Conversation

Two years ago, we were up talking at about One.

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?

Me: Yup...

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.


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