UNSOLVED PROBLEMS

In Number Theory, Logic, and Cryptography

Grimm’s Conjecture

 

Grimm's conjecture states that to each element of a set of consecutive composite numbers one can assign a distinct prime that divides it. 

For example, for the range 242 to 250, one can assign distinct primes as follows:

242: 11  243: 244: 61  245: 246: 41  247: 13  248: 31  249: 83  250: 5    

 

The problem is to prove the conjecture, or find a counter-example.

  

For further information, please see:

[1] http://en.wikipedia.org/wiki/Grimm's_conjecture

[2] http://mathworld.wolfram.com/GrimmsConjecture.html

[3] http://www.primepuzzles.net/puzzles/puzz_430.htm

 

You can check for contributions to this problem on the solutions page.

 

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