**Op**as follows: take a three-digit number

**N=100*a+10*b+c**(a must be a non-zero digit) and evaluate

**Op(N)= N**

^{a}+N^{b}+N^{c};e.g.

**Op(203)= 203**

Op(102)= 102+1+10404=10507.

^{2}+203^{0}+203^{3}=8406637;Op(102)= 102+1+10404=10507.

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).

2. Op(501)>3.15*10

^{13}.

3. Op(990)>1.82*10

^{27}.

4.

**http://www.walter-fendt.de/m14e/primes.htm**

links to a list of all primes below 10

^{12}.

Good luck.