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On particular sets of primes
Is the asymptotic density of powers of primes zero?Is there a one-to-one function from the natural numbers to the primes?How does the fact that Fermat primes are relatively prime imply there are infinite primes?Is this new method to find primes?An open problem on special primesAre there primes of every possible number of digits?Equations involving the Euler's totient function and Mersenne primesPrimes of form $6n-1$What fraction of primes are $3 (mod 4)$?Targeting all prime numbers with a minimal set of sinusoidal functions
$begingroup$
Let $f,g:mathbbNtomathbbN$ are two functions. Let $p$ be a prime such that
1) $#leftpleq x=+infty textas xtoinfty$
2) $#left g(p) textis also primeright=+infty textas xtoinfty$
My question is: does 1) and 2) implies that
1) $#leftf(p) textand g(p) textare primesright=+infty textas xtoinfty$
elementary-number-theory distribution-of-primes
asked Mar 22 at 14:50
Theory NombreTheory Nombre
1267
$endgroup$
add a comment |
$begingroup$
Let $f,g:mathbbNtomathbbN$ are two functions. Let $p$ be a prime such that
1) $#leftpleq x=+infty textas xtoinfty$
2) $#left g(p) textis also primeright=+infty textas xtoinfty$
My question is: does 1) and 2) implies that
1) $#leftf(p) textand g(p) textare primesright=+infty textas xtoinfty$
elementary-number-theory distribution-of-primes
asked Mar 22 at 14:50
Theory NombreTheory Nombre
1267
$endgroup$
$begingroup$
You fix a prime $p$, then make a condition that $f(p)$ is a prime. That doesn't make much sense. Do you maybe mean $f(x)$ is prime?
$endgroup$
– Dirk
Mar 22 at 14:54
$begingroup$
Yes $f(p)$ maybe prime.
$endgroup$
– Theory Nombre
Mar 22 at 14:59
add a comment |
$begingroup$
Let $f,g:mathbbNtomathbbN$ are two functions. Let $p$ be a prime such that
1) $#leftpleq x=+infty textas xtoinfty$
2) $#left g(p) textis also primeright=+infty textas xtoinfty$
My question is: does 1) and 2) implies that
1) $#leftf(p) textand g(p) textare primesright=+infty textas xtoinfty$
elementary-number-theory distribution-of-primes
asked Mar 22 at 14:50
Theory NombreTheory Nombre
1267
$endgroup$
Let $f,g:mathbbNtomathbbN$ are two functions. Let $p$ be a prime such that
1) $#leftpleq x=+infty textas xtoinfty$
2) $#left g(p) textis also primeright=+infty textas xtoinfty$
My question is: does 1) and 2) implies that
1) $#leftf(p) textand g(p) textare primesright=+infty textas xtoinfty$
elementary-number-theory distribution-of-primes
elementary-number-theory distribution-of-primes
asked Mar 22 at 14:50
Theory NombreTheory Nombre
1267
asked Mar 22 at 14:50
Theory NombreTheory Nombre
1267
asked Mar 22 at 14:50
Theory NombreTheory Nombre
1267
asked Mar 22 at 14:50
Theory NombreTheory Nombre
1267
asked Mar 22 at 14:50
Theory NombreTheory Nombre
1267
1267
$begingroup$
You fix a prime $p$, then make a condition that $f(p)$ is a prime. That doesn't make much sense. Do you maybe mean $f(x)$ is prime?
$endgroup$
– Dirk
Mar 22 at 14:54
$begingroup$
Yes $f(p)$ maybe prime.
$endgroup$
– Theory Nombre
Mar 22 at 14:59
add a comment |
$begingroup$
You fix a prime $p$, then make a condition that $f(p)$ is a prime. That doesn't make much sense. Do you maybe mean $f(x)$ is prime?
$endgroup$
– Dirk
Mar 22 at 14:54
$begingroup$
Yes $f(p)$ maybe prime.
$endgroup$
– Theory Nombre
Mar 22 at 14:59
$begingroup$
You fix a prime $p$, then make a condition that $f(p)$ is a prime. That doesn't make much sense. Do you maybe mean $f(x)$ is prime?
$endgroup$
– Dirk
Mar 22 at 14:54
$begingroup$
You fix a prime $p$, then make a condition that $f(p)$ is a prime. That doesn't make much sense. Do you maybe mean $f(x)$ is prime?
$endgroup$
– Dirk
Mar 22 at 14:54
$begingroup$
Yes $f(p)$ maybe prime.
$endgroup$
– Theory Nombre
Mar 22 at 14:59
$begingroup$
Yes $f(p)$ maybe prime.
$endgroup$
– Theory Nombre
Mar 22 at 14:59
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
No. Let the primes be enumerated as $p_i$.
Then $f(p_2i) = p_2i$, and $f(n) = 0$ otherwise, and $g(p_2i+1) = p_2i+1$ and $g(n)=0$ otherwise are counterexamples.
answered Mar 22 at 15:14
user113102user113102
4214
$endgroup$
$begingroup$
Simple and great. +1
$endgroup$
– ajotatxe
Mar 22 at 15:15
add a comment |
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1 Answer
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1 Answer
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$begingroup$
No. Let the primes be enumerated as $p_i$.
Then $f(p_2i) = p_2i$, and $f(n) = 0$ otherwise, and $g(p_2i+1) = p_2i+1$ and $g(n)=0$ otherwise are counterexamples.
answered Mar 22 at 15:14
user113102user113102
4214
$endgroup$
$begingroup$
Simple and great. +1
$endgroup$
– ajotatxe
Mar 22 at 15:15
add a comment |
$begingroup$
No. Let the primes be enumerated as $p_i$.
Then $f(p_2i) = p_2i$, and $f(n) = 0$ otherwise, and $g(p_2i+1) = p_2i+1$ and $g(n)=0$ otherwise are counterexamples.
answered Mar 22 at 15:14
user113102user113102
4214
$endgroup$
$begingroup$
Simple and great. +1
$endgroup$
– ajotatxe
Mar 22 at 15:15
add a comment |
$begingroup$
No. Let the primes be enumerated as $p_i$.
Then $f(p_2i) = p_2i$, and $f(n) = 0$ otherwise, and $g(p_2i+1) = p_2i+1$ and $g(n)=0$ otherwise are counterexamples.
answered Mar 22 at 15:14
user113102user113102
4214
$endgroup$
No. Let the primes be enumerated as $p_i$.
Then $f(p_2i) = p_2i$, and $f(n) = 0$ otherwise, and $g(p_2i+1) = p_2i+1$ and $g(n)=0$ otherwise are counterexamples.
answered Mar 22 at 15:14
user113102user113102
4214
answered Mar 22 at 15:14
user113102user113102
4214
answered Mar 22 at 15:14
user113102user113102
4214
answered Mar 22 at 15:14
user113102user113102
4214
4214
$begingroup$
Simple and great. +1
$endgroup$
– ajotatxe
Mar 22 at 15:15
add a comment |
$begingroup$
Simple and great. +1
$endgroup$
– ajotatxe
Mar 22 at 15:15
$begingroup$
Simple and great. +1
$endgroup$
– ajotatxe
Mar 22 at 15:15
$begingroup$
Simple and great. +1
$endgroup$
– ajotatxe
Mar 22 at 15:15
add a comment |
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$begingroup$
You fix a prime $p$, then make a condition that $f(p)$ is a prime. That doesn't make much sense. Do you maybe mean $f(x)$ is prime?
$endgroup$
– Dirk
Mar 22 at 14:54
$begingroup$
Yes $f(p)$ maybe prime.
$endgroup$
– Theory Nombre
Mar 22 at 14:59