How to prove the existence of a prime number with elementary method?
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Suppose $A>5$ is an integer and there exists a prime number $p$ such that $A-2leq p^2<A$.
Show that there exists at least one prime number $q$ such that $p<q<A$.
This seems to be intuitive to me since $A$ and $p$ has large gap. How can we prove it?
number-theory prime-numbers
asked 2 hours ago
user3813057
25418
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up vote
1
down vote
favorite
Suppose $A>5$ is an integer and there exists a prime number $p$ such that $A-2leq p^2<A$.
Show that there exists at least one prime number $q$ such that $p<q<A$.
This seems to be intuitive to me since $A$ and $p$ has large gap. How can we prove it?
number-theory prime-numbers
asked 2 hours ago
user3813057
25418
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Suppose $A>5$ is an integer and there exists a prime number $p$ such that $A-2leq p^2<A$.
Show that there exists at least one prime number $q$ such that $p<q<A$.
This seems to be intuitive to me since $A$ and $p$ has large gap. How can we prove it?
number-theory prime-numbers
asked 2 hours ago
user3813057
25418
Suppose $A>5$ is an integer and there exists a prime number $p$ such that $A-2leq p^2<A$.
Show that there exists at least one prime number $q$ such that $p<q<A$.
This seems to be intuitive to me since $A$ and $p$ has large gap. How can we prove it?
number-theory prime-numbers
number-theory prime-numbers
asked 2 hours ago
user3813057
25418
asked 2 hours ago
user3813057
25418
asked 2 hours ago
user3813057
25418
asked 2 hours ago
user3813057
25418
asked 2 hours ago
user3813057
25418
25418
add a comment |
add a comment |
1 Answer
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up vote
4
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Using one version of Bertrand's Postulate, if $q$ is the next prime after $p$ then
$$p<q<2ple p^2<A .$$
answered 2 hours ago
David
67.3k663126
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
4
down vote
Using one version of Bertrand's Postulate, if $q$ is the next prime after $p$ then
$$p<q<2ple p^2<A .$$
answered 2 hours ago
David
67.3k663126
add a comment |
up vote
4
down vote
Using one version of Bertrand's Postulate, if $q$ is the next prime after $p$ then
$$p<q<2ple p^2<A .$$
answered 2 hours ago
David
67.3k663126
add a comment |
up vote
4
down vote
up vote
4
down vote
Using one version of Bertrand's Postulate, if $q$ is the next prime after $p$ then
$$p<q<2ple p^2<A .$$
answered 2 hours ago
David
67.3k663126
Using one version of Bertrand's Postulate, if $q$ is the next prime after $p$ then
$$p<q<2ple p^2<A .$$
answered 2 hours ago
David
67.3k663126
answered 2 hours ago
David
67.3k663126
answered 2 hours ago
David
67.3k663126
answered 2 hours ago
David
67.3k663126
67.3k663126
add a comment |
add a comment |
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