2008 iTest Problems/Problem 4
Contents
Problem
The difference between two prime numbers is 
. Find their sum.
Solution
We know that any prime number, excluding 
, is congruent to 
. Thus, if both of the primes are not , their difference would be congruent to 
. Because 
, one of the primes must be . It follows that the other prime must then be 
. Therefore, the sum of the two is 
.
Solution 2
Since the difference is , one number must be even for the difference to be even. is the only even prime number, and therefore is one of the two numbers. The other number is 
, and their sum: 
.
See Also
| 2008 iTest (Problems) | ||
| Preceded by: Problem 3 |
Followed by: Problem 5 | |
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