Mathematics

What two prime numbers equal 85 when added together?


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jjpace2015

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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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