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What two prime numbers equal 85 when added together?

User B H
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1 Answer

1 vote

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.

User David Gill
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7.5k points

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