What two prime numbers equal 85 when added together?
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 odd-number 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.