Are there infinitely many prime numbers of the form $p^2+4$ with $p$ prime? [closed]

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Let $p$ be a prime. Are there infinitely many prime numbers which are of the form $p$$^2$$+$$4$?

number-theory

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edited Jul 15 at 5:02

asked Jul 15 at 3:28

Pacifica

458

closed as off-topic by Alex Francisco, Morgan Rodgers, amWhy, José Carlos Santos, Xander Henderson Jul 15 at 18:34

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Alex Francisco, Morgan Rodgers, amWhy, José Carlos Santos, Xander Henderson

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Where is your attempt?
  – tien lee
  Jul 15 at 3:30
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Welcome to MSE! Your question will likely be better received if you show what you have tried to resolve the problem, and/or the context of the problem.
  – Sambo
  Jul 15 at 3:33
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I just put that, thank you.
  – Pacifica
  Jul 15 at 3:48
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $p^2+4 equiv -1(mod 6)$ only implies that if there are infintely or finitely many primes of the form $p^2+4$, then all of them will leave a remainder $5$ when divided by $6$.
  – Abhishek Bakshi
  Jul 15 at 4:31
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Alright, I deleted it.
  – Pacifica
  Jul 15 at 5:03
  

  
  
  
  

 | 
show 7 more comments

up vote
0
down vote

favorite

1

Let $p$ be a prime. Are there infinitely many prime numbers which are of the form $p$$^2$$+$$4$?

number-theory

share|cite|improve this question

edited Jul 15 at 5:02

asked Jul 15 at 3:28

Pacifica

458

closed as off-topic by Alex Francisco, Morgan Rodgers, amWhy, José Carlos Santos, Xander Henderson Jul 15 at 18:34

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Alex Francisco, Morgan Rodgers, amWhy, José Carlos Santos, Xander Henderson

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Where is your attempt?
  – tien lee
  Jul 15 at 3:30
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Welcome to MSE! Your question will likely be better received if you show what you have tried to resolve the problem, and/or the context of the problem.
  – Sambo
  Jul 15 at 3:33
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I just put that, thank you.
  – Pacifica
  Jul 15 at 3:48
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $p^2+4 equiv -1(mod 6)$ only implies that if there are infintely or finitely many primes of the form $p^2+4$, then all of them will leave a remainder $5$ when divided by $6$.
  – Abhishek Bakshi
  Jul 15 at 4:31
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Alright, I deleted it.
  – Pacifica
  Jul 15 at 5:03
  

  
  
  
  

 | 
show 7 more comments

up vote
0
down vote

favorite

1

up vote
0
down vote

favorite

1

1

Let $p$ be a prime. Are there infinitely many prime numbers which are of the form $p$$^2$$+$$4$?

number-theory

share|cite|improve this question

edited Jul 15 at 5:02

asked Jul 15 at 3:28

Pacifica

458

Let $p$ be a prime. Are there infinitely many prime numbers which are of the form $p$$^2$$+$$4$?

number-theory

share|cite|improve this question

edited Jul 15 at 5:02

asked Jul 15 at 3:28

Pacifica

458

share|cite|improve this question

share|cite|improve this question

edited Jul 15 at 5:02

edited Jul 15 at 5:02

edited Jul 15 at 5:02

asked Jul 15 at 3:28

Pacifica

458

asked Jul 15 at 3:28

Pacifica

458

asked Jul 15 at 3:28

Pacifica

458

458

closed as off-topic by Alex Francisco, Morgan Rodgers, amWhy, José Carlos Santos, Xander Henderson Jul 15 at 18:34

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Alex Francisco, Morgan Rodgers, amWhy, José Carlos Santos, Xander Henderson

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by Alex Francisco, Morgan Rodgers, amWhy, José Carlos Santos, Xander Henderson Jul 15 at 18:34

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Alex Francisco, Morgan Rodgers, amWhy, José Carlos Santos, Xander Henderson

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Where is your attempt?
  – tien lee
  Jul 15 at 3:30
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Welcome to MSE! Your question will likely be better received if you show what you have tried to resolve the problem, and/or the context of the problem.
  – Sambo
  Jul 15 at 3:33
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I just put that, thank you.
  – Pacifica
  Jul 15 at 3:48
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $p^2+4 equiv -1(mod 6)$ only implies that if there are infintely or finitely many primes of the form $p^2+4$, then all of them will leave a remainder $5$ when divided by $6$.
  – Abhishek Bakshi
  Jul 15 at 4:31
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Alright, I deleted it.
  – Pacifica
  Jul 15 at 5:03
  

  
  
  
  

 | 
show 7 more comments

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Where is your attempt?
  – tien lee
  Jul 15 at 3:30
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Welcome to MSE! Your question will likely be better received if you show what you have tried to resolve the problem, and/or the context of the problem.
  – Sambo
  Jul 15 at 3:33
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I just put that, thank you.
  – Pacifica
  Jul 15 at 3:48
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $p^2+4 equiv -1(mod 6)$ only implies that if there are infintely or finitely many primes of the form $p^2+4$, then all of them will leave a remainder $5$ when divided by $6$.
  – Abhishek Bakshi
  Jul 15 at 4:31
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Alright, I deleted it.
  – Pacifica
  Jul 15 at 5:03
  

  
  
  
  

1

1

Where is your attempt?
– tien lee
Jul 15 at 3:30

Where is your attempt?
– tien lee
Jul 15 at 3:30

Welcome to MSE! Your question will likely be better received if you show what you have tried to resolve the problem, and/or the context of the problem.
– Sambo
Jul 15 at 3:33

Welcome to MSE! Your question will likely be better received if you show what you have tried to resolve the problem, and/or the context of the problem.
– Sambo
Jul 15 at 3:33

I just put that, thank you.
– Pacifica
Jul 15 at 3:48

I just put that, thank you.
– Pacifica
Jul 15 at 3:48

$p^2+4 equiv -1(mod 6)$ only implies that if there are infintely or finitely many primes of the form $p^2+4$, then all of them will leave a remainder $5$ when divided by $6$.
– Abhishek Bakshi
Jul 15 at 4:31

$p^2+4 equiv -1(mod 6)$ only implies that if there are infintely or finitely many primes of the form $p^2+4$, then all of them will leave a remainder $5$ when divided by $6$.
– Abhishek Bakshi
Jul 15 at 4:31

1

1

Alright, I deleted it.
– Pacifica
Jul 15 at 5:03

Alright, I deleted it.
– Pacifica
Jul 15 at 5:03

 | 
show 7 more comments

1 Answer
1

active

oldest

votes

up vote
5
down vote



accepted

The easy answer: We don't know.

Check out: https://oeis.org/A045637.

It looks like this problem is open but an answer would follow from us resolving the Bunyakovsky conjecture. You can read up on that here or on wiki.

share|cite|improve this answer

answered Jul 15 at 5:40

Mason

1,2401224

• 
  
  
  

  
  

  
  
  
  
  
  

  
  This is a field which has full of conjectures.
  – Pacifica
  Jul 15 at 6:59
  

  
  
  
  

add a comment | 

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
5
down vote



accepted

The easy answer: We don't know.

Check out: https://oeis.org/A045637.

It looks like this problem is open but an answer would follow from us resolving the Bunyakovsky conjecture. You can read up on that here or on wiki.

share|cite|improve this answer

answered Jul 15 at 5:40

Mason

1,2401224

• 
  
  
  

  
  

  
  
  
  
  
  

  
  This is a field which has full of conjectures.
  – Pacifica
  Jul 15 at 6:59
  

  
  
  
  

add a comment | 

up vote
5
down vote



accepted

The easy answer: We don't know.

Check out: https://oeis.org/A045637.

It looks like this problem is open but an answer would follow from us resolving the Bunyakovsky conjecture. You can read up on that here or on wiki.

share|cite|improve this answer

answered Jul 15 at 5:40

Mason

1,2401224

• 
  
  
  

  
  

  
  
  
  
  
  

  
  This is a field which has full of conjectures.
  – Pacifica
  Jul 15 at 6:59
  

  
  
  
  

add a comment | 

up vote
5
down vote



accepted

up vote
5
down vote



accepted

The easy answer: We don't know.

Check out: https://oeis.org/A045637.

It looks like this problem is open but an answer would follow from us resolving the Bunyakovsky conjecture. You can read up on that here or on wiki.

share|cite|improve this answer

answered Jul 15 at 5:40

Mason

1,2401224

The easy answer: We don't know.

Check out: https://oeis.org/A045637.

It looks like this problem is open but an answer would follow from us resolving the Bunyakovsky conjecture. You can read up on that here or on wiki.

share|cite|improve this answer

answered Jul 15 at 5:40

Mason

1,2401224

share|cite|improve this answer

share|cite|improve this answer

answered Jul 15 at 5:40

Mason

1,2401224

answered Jul 15 at 5:40

Mason

1,2401224

answered Jul 15 at 5:40

Mason

1,2401224

1,2401224

• 
  
  
  

  
  

  
  
  
  
  
  

  
  This is a field which has full of conjectures.
  – Pacifica
  Jul 15 at 6:59
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  This is a field which has full of conjectures.
  – Pacifica
  Jul 15 at 6:59
  

  
  
  
  

This is a field which has full of conjectures.
– Pacifica
Jul 15 at 6:59

This is a field which has full of conjectures.
– Pacifica
Jul 15 at 6:59

add a comment |