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Prime numbers that are the sum of two primes


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38 minutes ago, 0111narwhalz said:

Better get in early, before all the easy numbers get taken!

7 (5+2)

I just noticed a limitation.

All prime numbers, except 2 are odd. Furthermore, if you add two odd numbers, you get an even number, which are never prime numbers. This means that, to get an odd number, you need both an odd and even number. Since the only even prime number is 2, all the prime numbers that can be formed from the sum of two primes have a two in their sum.

Let n be a prime number. Because of all the reasons listed above, the only solution is to do 2+(n-2). Because n-2 must be a prime number, prime numbers that are the sum of two prime numbers have to have a prime number n and a prime number n-2. This means that they must be part of a double prime (the greater of the two). This makes this thread unnecessarily easy and almost completely useless. I rest my case.

Edited by mabdi36
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2 hours ago, mabdi36 said:

I just noticed a limitation.

All prime numbers, except 2 are odd. Furthermore, if you add two odd numbers, you get an even number, which are never prime numbers. This means that, to get an odd number, you need both an odd and even number. Since the only even prime number is 2, all the prime numbers that can be formed from the sum of two primes have a two in their sum.

Let n be a prime number. Because of all the reasons listed above, the only solution is to do 2+(n-2). Because n-2 must be a prime number, prime numbers that are the sum of two prime numbers have to have a prime number n and a prime number n-2. This means that they must be part of a double prime (the greater of the two). This makes this thread unnecessarily easy and almost completely useless. I rest my case.

You could open it up to primes that are the sum of any set of primes. If you add three odd numbers together you can have whatever parity you like.

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  • 4 weeks later...
On 12/8/2018 at 4:05 PM, mabdi36 said:

This makes this thread unnecessarily easy and almost completely useless.

 

On 12/8/2018 at 6:43 PM, 0111narwhalz said:

You could open it up to primes that are the sum of any set of primes.

So, 2+2+7 = 11 is a valid entry in this thread ?

Edited by YNM
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12 minutes ago, 0111narwhalz said:

It would be, if the rules were to be changed.

yeah... otherwise we'd just be pairing up twin primes...

even then it's still a pretty boring game.

Edited by YNM
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3 hours ago, mabdi36 said:

how do i get a mod to lock this thread?

You ask us to.  ;)

(For future reference:  if you've got a request for moderator action, the best way to do that is to file a report-- with an appropriate note, of course.  For example, in this case, if you wanted to lock your own thread, you could have just reported your OP with a note "hi, could you please lock my thread".  By filing the report, that pings the moderator team so whichever one of us happens to be online will get notified and can take care of it.)

Anyway, here ya go!

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