Mixing
Maximum $m$ verify $n+m$ coprime to primorial $q$?
$begingroup$
Let $n in mathbb{N}^{*}$ and $q geq 3$ a prime,
Suppose that $n$ coprime to $displaystyle {smallleft(prod_{substack{a leq q \ text{a prime}}} {normalsize a} right)}$ , after many observations i think that exists $m$ verify $n+m$ coprime to $displaystyle {smallleft(prod_{substack{a leq q \ text{a prime}}} {normalsize a} right)}$ and $m < 2q$, i am not sure about this claim and i like to know if there are results about that ?
number-theory prime-numbers
asked Jan 27 at 22:01
LAGRIDALAGRIDA
295111
$endgroup$
add a comment |
$begingroup$
Let $n in mathbb{N}^{*}$ and $q geq 3$ a prime,
Suppose that $n$ coprime to $displaystyle {smallleft(prod_{substack{a leq q \ text{a prime}}} {normalsize a} right)}$ , after many observations i think that exists $m$ verify $n+m$ coprime to $displaystyle {smallleft(prod_{substack{a leq q \ text{a prime}}} {normalsize a} right)}$ and $m < 2q$, i am not sure about this claim and i like to know if there are results about that ?
number-theory prime-numbers
asked Jan 27 at 22:01
LAGRIDALAGRIDA
295111
$endgroup$
2
$begingroup$
You are asking whether the Jacobsthal function $h(n)$ defined here is smaller than $2p_n$. If I'm not mistaken, the values given in this link give that this is false for $p_n=43$, hence so is your conjecture for $q=43$.
$endgroup$
– Wojowu
Jan 27 at 22:14
$begingroup$
Thanks, @Wojowu, and most possible that $h(n) > c p_n$ with $c$ arbiratery large.
$endgroup$
– LAGRIDA
Jan 28 at 11:21
add a comment |
$begingroup$
Let $n in mathbb{N}^{*}$ and $q geq 3$ a prime,
Suppose that $n$ coprime to $displaystyle {smallleft(prod_{substack{a leq q \ text{a prime}}} {normalsize a} right)}$ , after many observations i think that exists $m$ verify $n+m$ coprime to $displaystyle {smallleft(prod_{substack{a leq q \ text{a prime}}} {normalsize a} right)}$ and $m < 2q$, i am not sure about this claim and i like to know if there are results about that ?
number-theory prime-numbers
asked Jan 27 at 22:01
LAGRIDALAGRIDA
295111
$endgroup$
Let $n in mathbb{N}^{*}$ and $q geq 3$ a prime,
Suppose that $n$ coprime to $displaystyle {smallleft(prod_{substack{a leq q \ text{a prime}}} {normalsize a} right)}$ , after many observations i think that exists $m$ verify $n+m$ coprime to $displaystyle {smallleft(prod_{substack{a leq q \ text{a prime}}} {normalsize a} right)}$ and $m < 2q$, i am not sure about this claim and i like to know if there are results about that ?
number-theory prime-numbers
number-theory prime-numbers
asked Jan 27 at 22:01
LAGRIDALAGRIDA
295111
asked Jan 27 at 22:01
LAGRIDALAGRIDA
295111
edited Jan 27 at 22:15
LAGRIDA
asked Jan 27 at 22:01
LAGRIDALAGRIDA
295111
asked Jan 27 at 22:01
LAGRIDALAGRIDA
295111
asked Jan 27 at 22:01
LAGRIDALAGRIDA
295111
295111
2
$begingroup$
You are asking whether the Jacobsthal function $h(n)$ defined here is smaller than $2p_n$. If I'm not mistaken, the values given in this link give that this is false for $p_n=43$, hence so is your conjecture for $q=43$.
$endgroup$
– Wojowu
Jan 27 at 22:14
$begingroup$
Thanks, @Wojowu, and most possible that $h(n) > c p_n$ with $c$ arbiratery large.
$endgroup$
– LAGRIDA
Jan 28 at 11:21
add a comment |
2
$begingroup$
You are asking whether the Jacobsthal function $h(n)$ defined here is smaller than $2p_n$. If I'm not mistaken, the values given in this link give that this is false for $p_n=43$, hence so is your conjecture for $q=43$.
$endgroup$
– Wojowu
Jan 27 at 22:14
$begingroup$
Thanks, @Wojowu, and most possible that $h(n) > c p_n$ with $c$ arbiratery large.
$endgroup$
– LAGRIDA
Jan 28 at 11:21
2
2
$begingroup$
You are asking whether the Jacobsthal function $h(n)$ defined here is smaller than $2p_n$. If I'm not mistaken, the values given in this link give that this is false for $p_n=43$, hence so is your conjecture for $q=43$.
$endgroup$
– Wojowu
Jan 27 at 22:14
$begingroup$
You are asking whether the Jacobsthal function $h(n)$ defined here is smaller than $2p_n$. If I'm not mistaken, the values given in this link give that this is false for $p_n=43$, hence so is your conjecture for $q=43$.
$endgroup$
– Wojowu
Jan 27 at 22:14
$begingroup$
Thanks, @Wojowu, and most possible that $h(n) > c p_n$ with $c$ arbiratery large.
$endgroup$
– LAGRIDA
Jan 28 at 11:21
$begingroup$
Thanks, @Wojowu, and most possible that $h(n) > c p_n$ with $c$ arbiratery large.
$endgroup$
– LAGRIDA
Jan 28 at 11:21
add a comment |
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$begingroup$
You are asking whether the Jacobsthal function $h(n)$ defined here is smaller than $2p_n$. If I'm not mistaken, the values given in this link give that this is false for $p_n=43$, hence so is your conjecture for $q=43$.
$endgroup$
– Wojowu
Jan 27 at 22:14
$begingroup$
Thanks, @Wojowu, and most possible that $h(n) > c p_n$ with $c$ arbiratery large.
$endgroup$
– LAGRIDA
Jan 28 at 11:21