Can anyone please verify/review this proof about primes?

[Math100]

Homework Statement

It has been conjectured that there are infinitely many primes of the form n^2-2. Exhibit five such primes.

Relevant Equations

None.

Proof: Suppose that there are infinitely many primes of the form n^2-2.
Then we have n^2-2=2^2-2=2,
n^2-2=3^2-2=7,
n^2-2=5^2-2=23,
n^2-2=7^2-2=47,
n^2-2=9^2-2=79.
Note that 2, 7, 23, 47, 79 are prime numbers.
Therefore, five such primes are 2, 7, 23, 47, 79.

Above is my proof/answer for this problem. Can anyone please review/verify it and tell me if it's correct?

 

[fresh_42]

Correct. 167 is another one.

 

[Math100]

Correct. 167 is another one.

Yes, since 13^2-2=169-2=167.

 

[Math100]

Thank you so much for confirming.

 

[hutchphd]

Six down, infinity to go...

 

[FactChecker]

Homework Statement:: It has been conjectured that there are infinitely many primes of the form n^2-2. Exhibit five such primes.
Relevant Equations:: None.

Proof: Suppose that there are infinitely many primes of the form n^2-2.
Then we have n^2-2=2^2-2=2,
n^2-2=3^2-2=7,
n^2-2=5^2-2=23,
n^2-2=7^2-2=47,
n^2-2=9^2-2=79.
Note that 2, 7, 23, 47, 79 are prime numbers.
Therefore, five such primes are 2, 7, 23, 47, 79.

Above is my proof/answer for this problem. Can anyone please review/verify it and tell me if it's correct?

I am puzzled. What part of this did you have trouble verifying? Checking your own work is an important part of learning math.

 

[Math100]

I am puzzled. What part of this did you have trouble verifying? Checking your own work is an important part of learning math.

I just want to make sure if my proof is perfect and correct, because my textbook doesn't provide answers. And I want to get confirmation from experts.