What two prime numbers equal 85 when added together?
Mathematics
Joey123456789joe
Question
What two prime numbers equal 85 when added together?
1 Answer

1. User Answers AL2006
I started out trying to subtract a prime number from 85, and then
see whether I had a prime number remaining. I did this several
times, before I slapped myself upside the head.
 85 is an odd number.
 To get an oddnumber for a sum, you have to add one odd number
to one even number ... there's no other way.
 So one of the prime numbers we're looking for must be
an even number.
 The ONLY even number that's a prime number is ' 2 '.
So it must be one of them.
 Subtract 2 from 85, and you have 83 left.
Is 83 a prime number ? Yes.
 So the two numbers are 2 and 83.
If 83 were not a prime number, this wouldn't work, and I would have said
"There is no such pair of numbers.". That means it doesn't necessarily work
for every odd number.
Examples:
75 ===> 2 and 73 . \
55 ===> 2 and 53 . \
45 ===> 2 and 43 . \
Both primes. It works.
65 ===> 2 and 63 . 63 is not a prime. \
35 ===> 2 and 33 . 33 in not a prime. \
It doesn't work.