Then I wrote the checker to see if all multiples are present, and indeed 19 and 383 worked.
Next item on that list was 32327, which is too big. So I just guessed that maybe the first primes after 1000 would work instead. 1009 and 1013 didn't work, but 1019 worked. Proof by AC!
What made you think of decimal expansion when solving A? I OEIS'ed it :(
I brute forced when X and 2*X have a lot of digits in common, and searched the digit sequence in OEIS. Found decimal expansion of 19
It also referred me here, to try 383 after 19: magic-square-something
Then I wrote the checker to see if all multiples are present, and indeed 19 and 383 worked.
Next item on that list was 32327, which is too big. So I just guessed that maybe the first primes after 1000 would work instead. 1009 and 1013 didn't work, but 1019 worked. Proof by AC!