The goal of this program is to find all unique ways to
represent a given even number as the sum of two prime numbers.
A prime number is an integer greater than that is evenly divisible by only
itself and . The first
few prime numbers are ,
, , , , …. The German mathematician
Christian Goldbach (1690-1764) conjectured that every even
number greater than
can be represented by the sum of two prime numbers. (This
conjecture has never been proved nor has a counterexample ever
been found. As such, you may assume it is true for the cases
considered in this problem.) There may be several ways to
represent a given even number by the sum of primes. For
example, the even number may be represented as
, , or .
Input
Input starts with an integer () indicating the number of cases. The
following lines each
contain a test case of a single even number ().
Output
For each test case ,
give the number of unique ways that can be represented as a sum of two
primes. Then list the sums (one sum per line) in increasing
order of the first addend. The first addend must always be less
than or equal to the second to avoid duplicates. Print a blank
line after each test case.
Sample Input 1 |
Sample Output 1 |
3
4
26
100
|
4 has 1 representation(s)
2+2
26 has 3 representation(s)
3+23
7+19
13+13
100 has 6 representation(s)
3+97
11+89
17+83
29+71
41+59
47+53
|