SOLUTION: What is the only prime number that is the sum and difference of two primes?

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Question 269079: What is the only prime number that is the sum and difference of two primes?
Answer by mananth(16946) About Me  (Show Source):
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What is the only prime number that is the sum and difference of two primes?

let one digit be x and the other be y
xy=7 --------------1
x+y=8--------------2
multiply equation 2 by y
xy+y^2 = 8y ---------- 3
subtract 2 from 1
-y^2 = 7-8y
y^2-8y+7=0
y^2-7y-y+7=0
y(y-7)-1(y-7)=0
(y-1)(y-7)=0
y= 7 or 1
y cannot be in the tens place because the number is less than 50.
So the number will be 17