is it true that there **exist at least** a prime $P$ of the form...
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Given $k+1$ different prime numbers: $p_0,p_1,...,p_k$, with $p_0=2$ and $k>0$, is it true that there exist at least a prime $P$ such that all prime divisors of $P-1$ are only $p_0,p_1,...,p_k$ ? In other words, is it true that there is a prime $P$ of the form $p_0^{alpha_0}p_1^{alpha_1}p_2^{alpha_2}...p_k^{alpha_k}+1$ ?
I know this should be an open problem if I asked there exist infinitely many primes $P$ (I have asked here: is it true that there are infinitely many primes $P$ of the form $p_0^{alpha_0}p_1^{alpha_1}p_2^{alpha_2}...p_k^{alpha_k}+1$? , I may delete this question), since it is unclear whether there are infinitely many primes of the form $2^alpha +1$ or not (Fermat's prime). However, there is a least a prime of the form $2^alpha +1$, is $5$.
(Please let me know if this question is off-topic or should be closed)
number-theory
asked Dec 14 '18 at 16:48
appleapple
74015
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add a comment |
$begingroup$
Given $k+1$ different prime numbers: $p_0,p_1,...,p_k$, with $p_0=2$ and $k>0$, is it true that there exist at least a prime $P$ such that all prime divisors of $P-1$ are only $p_0,p_1,...,p_k$ ? In other words, is it true that there is a prime $P$ of the form $p_0^{alpha_0}p_1^{alpha_1}p_2^{alpha_2}...p_k^{alpha_k}+1$ ?
I know this should be an open problem if I asked there exist infinitely many primes $P$ (I have asked here: is it true that there are infinitely many primes $P$ of the form $p_0^{alpha_0}p_1^{alpha_1}p_2^{alpha_2}...p_k^{alpha_k}+1$? , I may delete this question), since it is unclear whether there are infinitely many primes of the form $2^alpha +1$ or not (Fermat's prime). However, there is a least a prime of the form $2^alpha +1$, is $5$.
(Please let me know if this question is off-topic or should be closed)
number-theory
asked Dec 14 '18 at 16:48
appleapple
74015
$endgroup$
add a comment |
$begingroup$
Given $k+1$ different prime numbers: $p_0,p_1,...,p_k$, with $p_0=2$ and $k>0$, is it true that there exist at least a prime $P$ such that all prime divisors of $P-1$ are only $p_0,p_1,...,p_k$ ? In other words, is it true that there is a prime $P$ of the form $p_0^{alpha_0}p_1^{alpha_1}p_2^{alpha_2}...p_k^{alpha_k}+1$ ?
I know this should be an open problem if I asked there exist infinitely many primes $P$ (I have asked here: is it true that there are infinitely many primes $P$ of the form $p_0^{alpha_0}p_1^{alpha_1}p_2^{alpha_2}...p_k^{alpha_k}+1$? , I may delete this question), since it is unclear whether there are infinitely many primes of the form $2^alpha +1$ or not (Fermat's prime). However, there is a least a prime of the form $2^alpha +1$, is $5$.
(Please let me know if this question is off-topic or should be closed)
number-theory
asked Dec 14 '18 at 16:48
appleapple
74015
$endgroup$
Given $k+1$ different prime numbers: $p_0,p_1,...,p_k$, with $p_0=2$ and $k>0$, is it true that there exist at least a prime $P$ such that all prime divisors of $P-1$ are only $p_0,p_1,...,p_k$ ? In other words, is it true that there is a prime $P$ of the form $p_0^{alpha_0}p_1^{alpha_1}p_2^{alpha_2}...p_k^{alpha_k}+1$ ?
I know this should be an open problem if I asked there exist infinitely many primes $P$ (I have asked here: is it true that there are infinitely many primes $P$ of the form $p_0^{alpha_0}p_1^{alpha_1}p_2^{alpha_2}...p_k^{alpha_k}+1$? , I may delete this question), since it is unclear whether there are infinitely many primes of the form $2^alpha +1$ or not (Fermat's prime). However, there is a least a prime of the form $2^alpha +1$, is $5$.
(Please let me know if this question is off-topic or should be closed)
number-theory
number-theory
asked Dec 14 '18 at 16:48
appleapple
74015
asked Dec 14 '18 at 16:48
appleapple
74015
asked Dec 14 '18 at 16:48
appleapple
74015
asked Dec 14 '18 at 16:48
appleapple
74015
asked Dec 14 '18 at 16:48
appleapple
74015
74015
add a comment |
add a comment |
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