Are there any other twin primes with this property?

In summary, the conversation discusses the property of twin primes where one half their sum results in a perfect number. The participants question if there are any other twin primes with this property and discuss the rarity of perfect numbers. It is concluded that there are no other twin primes with this property due to the divisibility of even perfect numbers by three.
  • #1
nikolany
4
0
The twin primes 5 and 7 are such that one half their sum is a perfect number. Are there any other twin primes with this property?

It works for p=5. I think it should be of the form 1/2*(p+P+2). Is this true? How can I prove it?

Thx
 
Physics news on Phys.org
  • #2
nikolany said:
Are there any other twin primes with this property?

I didn't find any. It's not too surprising, given how rare perfect numbers are.
 
  • #3
There aren't any more. An even perfect number (other than 6) is not divisible by three since it is the product of a power of 2 and a mersenne prime. Therefore one of P-1 or P+1 must be divisible by 3, and thus not prime.
 

1. What are twin primes?

Twin primes are a pair of prime numbers that differ by exactly 2, such as 3 and 5, 11 and 13, or 41 and 43.

2. What is the property being referred to?

The property being referred to is unknown, as the question is asking if there are any other twin primes with this unknown property.

3. How are twin primes related to this property?

The question is asking if there are any other twin primes that also possess this unknown property.

4. Is there any significance to finding other twin primes with this property?

It depends on the specific property being referred to. Some properties may have significant mathematical implications, while others may not.

5. How can one determine if other twin primes possess this property?

Without knowing the specific property, it is difficult to determine how to identify other twin primes with this property. It would likely involve analyzing the properties of twin primes and testing them against the unknown property.

Similar threads

I Frequency of prime number gaps according to (p-1)/(p-2)
    • Linear and Abstract Algebra
Replies
2
Views
800
Proof: Twin Primes Always Result in Perfect Squares
    • Calculus and Beyond Homework Help
Replies
3
Views
1K
Show that the sum of twin primes ## p ## and ## p+2 ## is divisible?
    • Precalculus Mathematics Homework Help
Replies
17
Views
2K
MHB Show that the groups are abelian
    • Linear and Abstract Algebra
Replies
1
Views
784
MHB Prove R is a Sub-ring of $\mathbb{Q}$ - Prime $p \in \mathbb{Z}$
    • Linear and Abstract Algebra
Replies
11
Views
1K
I Proof for a congruence relation
    • Linear and Abstract Algebra
Replies
17
Views
1K
Our Old Friend, the Twin Primes Conjecture
    • Linear and Abstract Algebra
Replies
11
Views
2K
I Confused about Gauss's Lemma of Irreducibility
    • Linear and Abstract Algebra
Replies
4
Views
1K
Proof of the twin primes conjecture
    • Linear and Abstract Algebra
Replies
4
Views
2K
Determine whether the integer 701 is prime by testing?
    • Calculus and Beyond Homework Help
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top