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Prime source (Posted on 2013-02-25) Difficulty: 5 of 5
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
Op(N)= Na+Nb+Nc;
e.g. Op(203)= 2032+2030+2033=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*1013.
3. Op(990)>1.82*1027.
4. http://www.walter-fendt.de/m14e/primes.htm
links to a list of all primes below 1012.

Good luck.

No Solution Yet Submitted by Ady TZIDON    
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  Subject Author Date
Solutioncomputer solutionCharlie2013-02-25 20:13:26
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