Can I efficiently enumerate all numbers in a range that have a prime factor in another given range?
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Suppose $a<b$ are positive integers. The object is to determine all the numbers $xin [a,b]$ having a prime factor in the range $[c,d]$ efficiently (that is without factoring all the numbers in the range or other brute-force approaches).
Example : Which numbers in the range $[40!-10^9,40!+10^9]$ have a prime factor in the range $8cdot 10^{15},10^{16}$ ?
number-theory elementary-number-theory prime-factorization
asked Dec 3 '18 at 18:49
PeterPeter
47.2k1039127
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add a comment |
$begingroup$
Suppose $a<b$ are positive integers. The object is to determine all the numbers $xin [a,b]$ having a prime factor in the range $[c,d]$ efficiently (that is without factoring all the numbers in the range or other brute-force approaches).
Example : Which numbers in the range $[40!-10^9,40!+10^9]$ have a prime factor in the range $8cdot 10^{15},10^{16}$ ?
number-theory elementary-number-theory prime-factorization
asked Dec 3 '18 at 18:49
PeterPeter
47.2k1039127
$endgroup$
1
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Just wondering: why would you need this?
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– YiFan
Dec 4 '18 at 5:13
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Some sort of sieving algorithm comes to mind. But I haven't heard of one that suits this specific scenario.
$endgroup$
– Klangen
Dec 18 '18 at 13:14
add a comment |
$begingroup$
Suppose $a<b$ are positive integers. The object is to determine all the numbers $xin [a,b]$ having a prime factor in the range $[c,d]$ efficiently (that is without factoring all the numbers in the range or other brute-force approaches).
Example : Which numbers in the range $[40!-10^9,40!+10^9]$ have a prime factor in the range $8cdot 10^{15},10^{16}$ ?
number-theory elementary-number-theory prime-factorization
asked Dec 3 '18 at 18:49
PeterPeter
47.2k1039127
$endgroup$
Suppose $a<b$ are positive integers. The object is to determine all the numbers $xin [a,b]$ having a prime factor in the range $[c,d]$ efficiently (that is without factoring all the numbers in the range or other brute-force approaches).
Example : Which numbers in the range $[40!-10^9,40!+10^9]$ have a prime factor in the range $8cdot 10^{15},10^{16}$ ?
number-theory elementary-number-theory prime-factorization
number-theory elementary-number-theory prime-factorization
asked Dec 3 '18 at 18:49
PeterPeter
47.2k1039127
asked Dec 3 '18 at 18:49
PeterPeter
47.2k1039127
asked Dec 3 '18 at 18:49
PeterPeter
47.2k1039127
asked Dec 3 '18 at 18:49
PeterPeter
47.2k1039127
asked Dec 3 '18 at 18:49
PeterPeter
47.2k1039127
47.2k1039127
1
$begingroup$
Just wondering: why would you need this?
$endgroup$
– YiFan
Dec 4 '18 at 5:13
$begingroup$
Some sort of sieving algorithm comes to mind. But I haven't heard of one that suits this specific scenario.
$endgroup$
– Klangen
Dec 18 '18 at 13:14
add a comment |
1
$begingroup$
Just wondering: why would you need this?
$endgroup$
– YiFan
Dec 4 '18 at 5:13
$begingroup$
Some sort of sieving algorithm comes to mind. But I haven't heard of one that suits this specific scenario.
$endgroup$
– Klangen
Dec 18 '18 at 13:14
1
1
$begingroup$
Just wondering: why would you need this?
$endgroup$
– YiFan
Dec 4 '18 at 5:13
$begingroup$
Just wondering: why would you need this?
$endgroup$
– YiFan
Dec 4 '18 at 5:13
$begingroup$
Some sort of sieving algorithm comes to mind. But I haven't heard of one that suits this specific scenario.
$endgroup$
– Klangen
Dec 18 '18 at 13:14
$begingroup$
Some sort of sieving algorithm comes to mind. But I haven't heard of one that suits this specific scenario.
$endgroup$
– Klangen
Dec 18 '18 at 13:14
add a comment |
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1
$begingroup$
Just wondering: why would you need this?
$endgroup$
– YiFan
Dec 4 '18 at 5:13
$begingroup$
Some sort of sieving algorithm comes to mind. But I haven't heard of one that suits this specific scenario.
$endgroup$
– Klangen
Dec 18 '18 at 13:14