I have three digits A B C, such that A is less than B, which is less than C. I can arrange these to form six different 3-digit numbers.
When A is at the start, both possible numbers (ABC and ACB) are prime.
When A is in the middle, both numbers are semi-prime (the product of two prime numbers).
When A is at the end, the number is either abundant by 71 (the sum of its proper divisors is 71 more than the number itself), or deficient by 226 (the sum of its proper divisors is 226 less than the number itself).
What are the three digits?