CS1101C Lab 2 (Even Week)

Goldbach's Conjecture

The name of your C program file must be called goldbach.c, files with any other name will not be marked.

Preliminary

In June 7, 1742, Christian Goldbach wrote a letter to Leonhard Euler in which he states that "at least it seems that every number that is greater than 2 is the sum of three primes". Goldbach considered 1 to be a prime, a convention which is no longer assumed. Euler later came up with an equivalent "strong" conjecture which asserts that all positive even integers greater than two can be expressed as the sum of two primes. This conjecture remains open till today as nobody has yet proved it. In the words of Goldbach himself: "I consider an entirely certain theorem in spite of that I am not able to demonstrate it."

The Task

Your task is to write a program goldbach.c that accepts a number and determine all possible pairs of sum of primes, apart from rearrangement. You will need to explicitly check that the number input by the user is even, as well as, greater than two.

Assuming that the executable is goldbach, a sample run of the program is shown below. User input is denoted in bold.

$ gcc -Wall goldbach.c -o goldbach
$ goldbach
Enter even number: 2
2 is not an even number greater than 2

$ goldbach
Enter even number: 3
3 is not an even number greater than 2

$ goldbach
Enter even number: 4
4 = 2 + 2

$ goldbach
Enter even number: 10
10 = 3 + 7
10 = 5 + 5

$ goldbach
Enter even number: 50
50 = 3 + 47
50 = 7 + 43
50 = 13 + 37
50 = 19 + 31

$ goldbach
Enter even number: 100
100 = 3 + 97
100 = 11 + 89
100 = 17 + 83
100 = 29 + 71
100 = 41 + 59
100 = 47 + 53

$ goldbach
Enter even number: 1234
1234 = 3 + 1231
1234 = 5 + 1229
1234 = 11 + 1223
1234 = 17 + 1217
1234 = 41 + 1193
1234 = 47 + 1187
1234 = 53 + 1181
1234 = 71 + 1163
1234 = 83 + 1151
1234 = 131 + 1103
1234 = 137 + 1097
1234 = 173 + 1061
1234 = 251 + 983
1234 = 257 + 977
1234 = 263 + 971
1234 = 281 + 953
1234 = 293 + 941
1234 = 347 + 887
1234 = 353 + 881
1234 = 461 + 773
1234 = 491 + 743
1234 = 557 + 677
1234 = 587 + 647
1234 = 593 + 641
1234 = 617 + 617

$

Points to Note

• For simplicity, we assume that user input will always be within the range of permissible values, so there is no need to perform any explicit checks on the data entered by the user.
• Do not use any other data types except int. That means you are not allowed to use double, float, char, etc. You are only allowed to use the int data type and nothing else.

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