Question

The sum of three prime numbers is 80. The difference between two of them is 4. Find the numbers.

Answer 1

The prime numbers must be below 80.

We can list the prime numbers as shown below.

We have :

2, 3, 5, 7 ,11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53,

the differences giving 4 are:

7 - 3 = 4

17 - 13 = 4

23 - 19 = 4

41 - 37 = 4

47 - 43 = 4

We take 41 and 37

their sum is :

41 + 37 = 78

we need 2 to make it 80.

78 + 2 = 80

So the numbers are :

2 , 37 ,41