The four values x, y, x−y and x+y are all positive prime integers. What is the sum of all the four integers?
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To find the sum of the four positive prime integers x, y, x−y, and x+y, we need to first determine their values.
Since x and y are prime integers, they must be greater than 1 and only divisible by 1 and themselves. Additionally, since x−y and x+y are also prime integers, it means that they are only divisible by 1 and themselves.
Let's consider the possible values of x and y:
1. If x is 2, then y can be any odd prime number greater than 1. In this case, x+y = 2+y and x−y = 2−y. Both 2+y and 2−y can be prime numbers as long as y is an odd prime number.
2. If x is an odd prime number greater than 2, then y must be 2, because the sum or difference of two odd prime numbers would be even and greater than 2, thus not prime.
Now, we can list the possible values and calculate their sum:
Case 1: x = 2 and y is an odd prime number greater than 1
In this case, the four numbers would be 2, y, 2−y, and 2+y.
Case 2: x is an odd prime number greater than 2 and y = 2
In this case, the four numbers would be x, 2, x−2, and x+2.
To find the sum, you need to calculate the sum of the four numbers for each case and add them together.
Please note that I cannot determine the specific values of x and y without more information.