A prime number which equals prime numbers

In summary: So (assuming I understand the question) one counter-example is enough to disprove the statement. In summary, it is not always true that the sum of prime numbers which equals to other prime numbers is a prime number. One counter-example, such as 3+11+61=75, is enough to disprove the statement.
  • #1
MathematicalPhysicist
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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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  • #2
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?
 
  • #3
i don't mean all the primes just a few.
those who does follow the statement.
 
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  • #4
Please give an example:

"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?
 
  • #5
All primes except 2 are odd. So if you add two of them, the result is even, and thus not a prime.
 
  • #6
Originally posted by HallsofIvy
Please give an example:

"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 isn't a prime.
example the sum of:
2+3=5
5+2=7
11+2=13
if you sum them you don't 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 don't equal to other primes.
 
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  • #7
Originally posted by loop quantum gravity
edit: a counter example is like 2 and 3 which are prime but they don't 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 :smile:, 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.
 
  • #8
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 general view, for example:
2+59=61
3+11+53=67
3+11+61=71

the sum of them is equal to prime number: 199.
 
  • #9
2+3=5
2+5=7
2+11=13

5+7+13=25
 
  • #10
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.
 
  • #11
MathematicalPhysicist said:
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.
 

1. What is a prime number?

A prime number is a positive integer that is only divisible by 1 and itself. In other words, it has no divisors other than 1 and itself.

2. Can a prime number equal another prime number?

Yes, there are prime numbers that are equal to each other, such as 3 and 3, or 11 and 11.

3. Are there any prime numbers that are equal to more than one other prime number?

No, every prime number can only be equal to one other prime number, which is itself.

4. How many prime numbers are equal to other prime numbers?

There are infinitely many prime numbers, and among them, there are also infinitely many pairs of prime numbers that are equal to each other.

5. Can a prime number be equal to a non-prime number?

No, a prime number can only be equal to another prime number. A non-prime number will have more divisors and therefore cannot equal a prime number.

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