In the following alphametic equation each capital letter in bold represents a different base x digit from 0 to x-1. None of the numbers can contain any leading zero.

                        PRIME + PRIME + PRIME = NUMBER

Determine the minimum positive integer value of x such that PRIME is a prime number.

Bonus Question:

What would have been the minimum positive integer value of x, if each capital letter in bold represented a different base x prime digit from 2 to x-1?

In base 14:     

                                                    decimal              
p   r  i   m  e         n  u   m  b  e   r       prime  number
5  13  4  12  9         1  3  12  0  9  13      228713  686139
10  9  13  1  3         2  4  1  11  3  9       411421  1234263
11  13  4  12  9        2  7  12  0  9  13      459209  1377627

Posted by Charlie on 2009-06-10 18:55:21