what two prime numbers why is 2 the only prime number why is two not a prime number are 2 and 3 prime numbers what two prime numbers make 30 what two prime numbers multiply to 95 what two prime numbers multiply to 85 what two prime numbers are in both 30 and 42 what two prime numbers add up to 24 what two prime numbers have a sum of 16 what two prime numbers have a sum of 7 what two prime numbers multiply to make 85 what two prime numbers multiply to make 95 what two prime numbers add up to 30 what two prime numbers multiply to make 65 what two prime numbers make 24 what two prime numbers make 85 what two prime numbers make 95 hcf of two co prime numbers what are two prime numbers that add to 30 sum of two prime numbers is always even what is the hcf of two prime numbers what and 2 are the first two prime numbers lcm of two prime numbers is the sum of two prime numbers always prime two prime numbers two prime numbers that add up to 30 two prime numbers that have a sum of 32

What two prime numbers equal 85 when added together?

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 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.

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