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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













0












$begingroup$


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) $#leftf(p) textand g(p) textare primesright=+infty textas xtoinfty$










share|cite|improve this question









$endgroup$











  • $begingroup$
    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















0












$begingroup$


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) $#leftf(p) textand g(p) textare primesright=+infty textas xtoinfty$










share|cite|improve this question









$endgroup$











  • $begingroup$
    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













0












0








0





$begingroup$


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) $#leftf(p) textand g(p) textare primesright=+infty textas xtoinfty$










share|cite|improve this question









$endgroup$




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






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










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
















  • $begingroup$
    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










1 Answer
1






active

oldest

votes


















2












$begingroup$

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.






share|cite|improve this answer









$endgroup$












  • $begingroup$
    Simple and great. +1
    $endgroup$
    – ajotatxe
    Mar 22 at 15:15











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1 Answer
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1 Answer
1






active

oldest

votes









active

oldest

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active

oldest

votes









2












$begingroup$

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.






share|cite|improve this answer









$endgroup$












  • $begingroup$
    Simple and great. +1
    $endgroup$
    – ajotatxe
    Mar 22 at 15:15















2












$begingroup$

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.






share|cite|improve this answer









$endgroup$












  • $begingroup$
    Simple and great. +1
    $endgroup$
    – ajotatxe
    Mar 22 at 15:15













2












2








2





$begingroup$

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.






share|cite|improve this answer









$endgroup$



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.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Mar 22 at 15:14









user113102user113102

4214




4214











  • $begingroup$
    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




$begingroup$
Simple and great. +1
$endgroup$
– ajotatxe
Mar 22 at 15:15

















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