Let us define an operation Op as follows: take a three-digit number N=100*a+10*b+c (a must be a non-zero digit) and evaluate
e.g. Op(203)= 2032+2030+2033=8406637;
The first example resulted in a prime number (8406637),
the second - a composite (10507=7*19*79).
A 3-digit number, which by means of Op(N) generates a prime we shall call a "prime source".
203 is a prime source.
101 is obviously the only
three digit number that generates a prime source !
Now, the D5 problem: Find the largest prime source.
Reducing the degree of difficulty, we shall deal with three "limited editions":
D2: What is the smallest prime source?
D2: What is the largest prime source you can get?
D4: Find the largest prime source below 500.
Some facts and hints:
1. Testing all 3-digit numbers is counter-productive - either the b digit or the c digit (but not both) must be 0, otherwise N either divides Op(N)(no zero digits) or is even (b=c=0).
to a list of all primes below 1012.