Squares, Cubes and Prime numbers
0
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Suppose $p$ and $p^2+2$ are prime numbers, prove that $p^3+2$ is also a prime number. Actually I do not know what is the relationship among square numbers, cube numbers and prime numbers
elementary-number-theory
asked Jul 20 '14 at 17:30
Achari S GaneshaAchari S Ganesha
4441923
$endgroup$
add a comment |
0
$begingroup$
Suppose $p$ and $p^2+2$ are prime numbers, prove that $p^3+2$ is also a prime number. Actually I do not know what is the relationship among square numbers, cube numbers and prime numbers
elementary-number-theory
asked Jul 20 '14 at 17:30
Achari S GaneshaAchari S Ganesha
4441923
$endgroup$
3
$begingroup$
This is a trick problem. There's only one such possible prime $p$ so that $p^2+2$ is prime...
$endgroup$
– Thomas Andrews
Jul 20 '14 at 17:34
$begingroup$
@ThomasAndrews what do you mean ? $3$ and $7$ seem to be such primes
$endgroup$
– Gabriel Romon
Jul 20 '14 at 17:36
$begingroup$
Is $7^2+2$ prime? @G.T.R
$endgroup$
– Thomas Andrews
Jul 20 '14 at 17:37
$begingroup$
Oops, my bad @ThomasAndrews
$endgroup$
– Gabriel Romon
Jul 20 '14 at 17:37
$begingroup$
math.stackexchange.com/questions/269790/… and math.stackexchange.com/questions/234077/prime-p-with-p28-prime
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– lab bhattacharjee
Jul 20 '14 at 17:53
add a comment |
0
0
0
$begingroup$
Suppose $p$ and $p^2+2$ are prime numbers, prove that $p^3+2$ is also a prime number. Actually I do not know what is the relationship among square numbers, cube numbers and prime numbers
elementary-number-theory
asked Jul 20 '14 at 17:30
Achari S GaneshaAchari S Ganesha
4441923
$endgroup$
Suppose $p$ and $p^2+2$ are prime numbers, prove that $p^3+2$ is also a prime number. Actually I do not know what is the relationship among square numbers, cube numbers and prime numbers
elementary-number-theory
elementary-number-theory
asked Jul 20 '14 at 17:30
Achari S GaneshaAchari S Ganesha
4441923
asked Jul 20 '14 at 17:30
Achari S GaneshaAchari S Ganesha
4441923
asked Jul 20 '14 at 17:30
Achari S GaneshaAchari S Ganesha
4441923
asked Jul 20 '14 at 17:30
Achari S GaneshaAchari S Ganesha
4441923
asked Jul 20 '14 at 17:30
Achari S GaneshaAchari S Ganesha
4441923
4441923
3
$begingroup$
This is a trick problem. There's only one such possible prime $p$ so that $p^2+2$ is prime...
$endgroup$
– Thomas Andrews
Jul 20 '14 at 17:34
$begingroup$
@ThomasAndrews what do you mean ? $3$ and $7$ seem to be such primes
$endgroup$
– Gabriel Romon
Jul 20 '14 at 17:36
$begingroup$
Is $7^2+2$ prime? @G.T.R
$endgroup$
– Thomas Andrews
Jul 20 '14 at 17:37
$begingroup$
Oops, my bad @ThomasAndrews
$endgroup$
– Gabriel Romon
Jul 20 '14 at 17:37
$begingroup$
math.stackexchange.com/questions/269790/… and math.stackexchange.com/questions/234077/prime-p-with-p28-prime
$endgroup$
– lab bhattacharjee
Jul 20 '14 at 17:53
add a comment |
3
$begingroup$
This is a trick problem. There's only one such possible prime $p$ so that $p^2+2$ is prime...
$endgroup$
– Thomas Andrews
Jul 20 '14 at 17:34
$begingroup$
@ThomasAndrews what do you mean ? $3$ and $7$ seem to be such primes
$endgroup$
– Gabriel Romon
Jul 20 '14 at 17:36
$begingroup$
Is $7^2+2$ prime? @G.T.R
$endgroup$
– Thomas Andrews
Jul 20 '14 at 17:37
$begingroup$
Oops, my bad @ThomasAndrews
$endgroup$
– Gabriel Romon
Jul 20 '14 at 17:37
$begingroup$
math.stackexchange.com/questions/269790/… and math.stackexchange.com/questions/234077/prime-p-with-p28-prime
$endgroup$
– lab bhattacharjee
Jul 20 '14 at 17:53
3
3
$begingroup$
This is a trick problem. There's only one such possible prime $p$ so that $p^2+2$ is prime...
$endgroup$
– Thomas Andrews
Jul 20 '14 at 17:34
$begingroup$
This is a trick problem. There's only one such possible prime $p$ so that $p^2+2$ is prime...
$endgroup$
– Thomas Andrews
Jul 20 '14 at 17:34
$begingroup$
@ThomasAndrews what do you mean ? $3$ and $7$ seem to be such primes
$endgroup$
– Gabriel Romon
Jul 20 '14 at 17:36
$begingroup$
@ThomasAndrews what do you mean ? $3$ and $7$ seem to be such primes
$endgroup$
– Gabriel Romon
Jul 20 '14 at 17:36
$begingroup$
Is $7^2+2$ prime? @G.T.R
$endgroup$
– Thomas Andrews
Jul 20 '14 at 17:37
$begingroup$
Is $7^2+2$ prime? @G.T.R
$endgroup$
– Thomas Andrews
Jul 20 '14 at 17:37
$begingroup$
Oops, my bad @ThomasAndrews
$endgroup$
– Gabriel Romon
Jul 20 '14 at 17:37
$begingroup$
Oops, my bad @ThomasAndrews
$endgroup$
– Gabriel Romon
Jul 20 '14 at 17:37
$begingroup$
math.stackexchange.com/questions/269790/… and math.stackexchange.com/questions/234077/prime-p-with-p28-prime
$endgroup$
– lab bhattacharjee
Jul 20 '14 at 17:53
$begingroup$
math.stackexchange.com/questions/269790/… and math.stackexchange.com/questions/234077/prime-p-with-p28-prime
$endgroup$
– lab bhattacharjee
Jul 20 '14 at 17:53
add a comment |
1 Answer
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Hint: if $p equiv pm 1 mod 3$, then what is $p^2 + 2 mod 3$? How many primes $p$ are there such that $p^2 + 2$ is also prime?
answered Jul 20 '14 at 17:32
Mathmo123Mathmo123
17.8k33165
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Hint: if $p equiv pm 1 mod 3$, then what is $p^2 + 2 mod 3$? How many primes $p$ are there such that $p^2 + 2$ is also prime?
answered Jul 20 '14 at 17:32
Mathmo123Mathmo123
17.8k33165
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0
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Hint: if $p equiv pm 1 mod 3$, then what is $p^2 + 2 mod 3$? How many primes $p$ are there such that $p^2 + 2$ is also prime?
answered Jul 20 '14 at 17:32
Mathmo123Mathmo123
17.8k33165
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Hint: if $p equiv pm 1 mod 3$, then what is $p^2 + 2 mod 3$? How many primes $p$ are there such that $p^2 + 2$ is also prime?
answered Jul 20 '14 at 17:32
Mathmo123Mathmo123
17.8k33165
$endgroup$
Hint: if $p equiv pm 1 mod 3$, then what is $p^2 + 2 mod 3$? How many primes $p$ are there such that $p^2 + 2$ is also prime?
answered Jul 20 '14 at 17:32
Mathmo123Mathmo123
17.8k33165
answered Jul 20 '14 at 17:32
Mathmo123Mathmo123
17.8k33165
answered Jul 20 '14 at 17:32
Mathmo123Mathmo123
17.8k33165
answered Jul 20 '14 at 17:32
Mathmo123Mathmo123
17.8k33165
17.8k33165
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3
$begingroup$
This is a trick problem. There's only one such possible prime $p$ so that $p^2+2$ is prime...
$endgroup$
– Thomas Andrews
Jul 20 '14 at 17:34
$begingroup$
@ThomasAndrews what do you mean ? $3$ and $7$ seem to be such primes
$endgroup$
– Gabriel Romon
Jul 20 '14 at 17:36
$begingroup$
Is $7^2+2$ prime? @G.T.R
$endgroup$
– Thomas Andrews
Jul 20 '14 at 17:37
$begingroup$
Oops, my bad @ThomasAndrews
$endgroup$
– Gabriel Romon
Jul 20 '14 at 17:37
$begingroup$
math.stackexchange.com/questions/269790/… and math.stackexchange.com/questions/234077/prime-p-with-p28-prime
$endgroup$
– lab bhattacharjee
Jul 20 '14 at 17:53