# A prime number which equals prime numbers

Gold Member
how can i proove or disproove that the sum of a prime numbers which equals to other prime numbers is a prime number?
i hope the question has been comprehended.

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Staff Emeritus
Gold Member
Dearly Missed
Your hope is in vain, at least in my case.

Let's see. 2+5 = 7 so the sum is prime. But 2+7 = 9, Oops.

Maybe successive primes? 2+5 = 7, 5+7 =12 Oops.

Maybe give an example?

Gold Member
i dont mean all the primes just a few.
those who does follow the statement.

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HallsofIvy
Homework Helper

"the sum of a prime numbers which equals to other prime numbers "
do you mean things like "2+ 5= 7", "9+ 2= 11", "5+ 7+ 11= 23"?

"is a prime number?" Is WHAT a prime a number?

My first reaction was that you meant the sum: well, of course, that's a prime- you just said it was!

I THINK you mean that the number of primes in the sum must be a prime. I'll have to think of that. Can we find 4 primes whose sum is a prime?

All primes except 2 are odd. So if you add two of them, the result is even, and thus not a prime.

Gold Member
Originally posted by HallsofIvy

"the sum of a prime numbers which equals to other prime numbers "
do you mean things like "2+ 5= 7", "9+ 2= 11", "5+ 7+ 11= 23"?

"is a prime number?" Is WHAT a prime a number?

My first reaction was that you meant the sum: well, of course, that's a prime- you just said it was!

I THINK you mean that the number of primes in the sum must be a prime. I'll have to think of that. Can we find 4 primes whose sum is a prime?
9 isnt a prime.
example the sum of:
2+3=5
5+2=7
11+2=13
if you sum them you dont get a prime 25 and thus you disproove the statement what i want is a generalized proof not munerical.
edit: a counter example is like 2 and 3 which are prime but they dont equal to other primes.

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Originally posted by loop quantum gravity
edit: a counter example is like 2 and 3 which are prime but they dont equal to other primes.
I don't know about others, but i don't understand what you mean by that.

Now, what i understand from what you previsouly said is that (in some cases) you can add up primes to reach another prime number. Now, some have showed that this is not always possible, some it is only possible in some cases.
What you want to proove is that (the fact sometimes you can add up primes to end up with primes).
So, in other words, if you take some primes, and add them up, you will reach one of two results :
1-a non-prime number
2-a prime number
You are choosing part 2 to study, and want to proove it.
What u are trying to proove is prooved by definition , you are saying that "among the add up of primes, i want to proove that those with a prime number result are prime numbers".
It is like saying "proove that primes are primes", which is proven by definition.
Maybe i didn't understand your question though.

Gold Member
no that's not what i want to find.
what i want to find is the sum of the prime numbers which equal other prime numbers and proove it or disproove it for the genral view, for example:
2+59=61
3+11+53=67
3+11+61=71

the sum of them is equal to prime number: 199.

2+3=5
2+5=7
2+11=13

5+7+13=25

HallsofIvy
Homework Helper
At first I thought the problem was that I didn't know what you were saying.

Now, I think the problem is that YOU don't know what you are saying!

Yes, the sum of SOME primes is prime. The sum of other primes is NOT.

It makes no sense to say that you want a GENERAL proof of something that is NOT generally true!

You may mean that you want to find conditions on the original set of primes so that you will know that the sum must be prime.

That is so general I doubt that you will find any simple conditions.

2+59=61
3+11+53=67
3+11+61=71

the sum of them is equal to prime number: 199.
This is an old thread - but just for the record:

3+11+61= 75 (not 71)

therefore 61+67+75= 203 which is not a prime.