Large Carmichael number
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I need to find or generate a very large Carmichael number (500 digits or longer). I've tried to find a database or just an example of such a number but failed. Is there any examples of really big Carmichael numbers or an implementation of an algorithm I'd be able to run locally?
number-theory algorithms carmichael-numbers
asked Dec 7 '18 at 11:22
NikromNikrom
1376
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add a comment |
$begingroup$
I need to find or generate a very large Carmichael number (500 digits or longer). I've tried to find a database or just an example of such a number but failed. Is there any examples of really big Carmichael numbers or an implementation of an algorithm I'd be able to run locally?
number-theory algorithms carmichael-numbers
asked Dec 7 '18 at 11:22
NikromNikrom
1376
$endgroup$
add a comment |
$begingroup$
I need to find or generate a very large Carmichael number (500 digits or longer). I've tried to find a database or just an example of such a number but failed. Is there any examples of really big Carmichael numbers or an implementation of an algorithm I'd be able to run locally?
number-theory algorithms carmichael-numbers
asked Dec 7 '18 at 11:22
NikromNikrom
1376
$endgroup$
I need to find or generate a very large Carmichael number (500 digits or longer). I've tried to find a database or just an example of such a number but failed. Is there any examples of really big Carmichael numbers or an implementation of an algorithm I'd be able to run locally?
number-theory algorithms carmichael-numbers
number-theory algorithms carmichael-numbers
asked Dec 7 '18 at 11:22
NikromNikrom
1376
asked Dec 7 '18 at 11:22
NikromNikrom
1376
asked Dec 7 '18 at 11:22
NikromNikrom
1376
asked Dec 7 '18 at 11:22
NikromNikrom
1376
asked Dec 7 '18 at 11:22
NikromNikrom
1376
1376
add a comment |
add a comment |
1 Answer
1
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Probably the best approach is to search a positive integer $k$, such that $6k+1$ , $12k+1$ , $18k+1$ are all prime. Then $$N=(6k+1)(12k+1)(18k+1)$$ is a Carmichael-number. If you find $k>10^{170}$ with the desired property , you are done.
answered Dec 7 '18 at 11:39
PeterPeter
48.6k1139136
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For example , $$k=10^{170}+8786356$$ does the job
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– Peter
Dec 7 '18 at 11:56
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I can confirm that it is a (probable) Carmichael number using a Pascal implementation of the algorithm from math.stackexchange.com/a/1729144/61216
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– gammatester
Dec 7 '18 at 12:04
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I tested the factors with the APR-test. They are in fact all prime.
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– Peter
Dec 7 '18 at 12:06
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hal.inria.fr/inria-00076980/document could be of interest to you.
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– Claude Leibovici
Dec 7 '18 at 12:25
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Probably the best approach is to search a positive integer $k$, such that $6k+1$ , $12k+1$ , $18k+1$ are all prime. Then $$N=(6k+1)(12k+1)(18k+1)$$ is a Carmichael-number. If you find $k>10^{170}$ with the desired property , you are done.
answered Dec 7 '18 at 11:39
PeterPeter
48.6k1139136
$endgroup$
$begingroup$
For example , $$k=10^{170}+8786356$$ does the job
$endgroup$
– Peter
Dec 7 '18 at 11:56
$begingroup$
I can confirm that it is a (probable) Carmichael number using a Pascal implementation of the algorithm from math.stackexchange.com/a/1729144/61216
$endgroup$
– gammatester
Dec 7 '18 at 12:04
$begingroup$
I tested the factors with the APR-test. They are in fact all prime.
$endgroup$
– Peter
Dec 7 '18 at 12:06
$begingroup$
hal.inria.fr/inria-00076980/document could be of interest to you.
$endgroup$
– Claude Leibovici
Dec 7 '18 at 12:25
add a comment |
$begingroup$
Probably the best approach is to search a positive integer $k$, such that $6k+1$ , $12k+1$ , $18k+1$ are all prime. Then $$N=(6k+1)(12k+1)(18k+1)$$ is a Carmichael-number. If you find $k>10^{170}$ with the desired property , you are done.
answered Dec 7 '18 at 11:39
PeterPeter
48.6k1139136
$endgroup$
$begingroup$
For example , $$k=10^{170}+8786356$$ does the job
$endgroup$
– Peter
Dec 7 '18 at 11:56
$begingroup$
I can confirm that it is a (probable) Carmichael number using a Pascal implementation of the algorithm from math.stackexchange.com/a/1729144/61216
$endgroup$
– gammatester
Dec 7 '18 at 12:04
$begingroup$
I tested the factors with the APR-test. They are in fact all prime.
$endgroup$
– Peter
Dec 7 '18 at 12:06
$begingroup$
hal.inria.fr/inria-00076980/document could be of interest to you.
$endgroup$
– Claude Leibovici
Dec 7 '18 at 12:25
add a comment |
$begingroup$
Probably the best approach is to search a positive integer $k$, such that $6k+1$ , $12k+1$ , $18k+1$ are all prime. Then $$N=(6k+1)(12k+1)(18k+1)$$ is a Carmichael-number. If you find $k>10^{170}$ with the desired property , you are done.
answered Dec 7 '18 at 11:39
PeterPeter
48.6k1139136
$endgroup$
Probably the best approach is to search a positive integer $k$, such that $6k+1$ , $12k+1$ , $18k+1$ are all prime. Then $$N=(6k+1)(12k+1)(18k+1)$$ is a Carmichael-number. If you find $k>10^{170}$ with the desired property , you are done.
answered Dec 7 '18 at 11:39
PeterPeter
48.6k1139136
edited Dec 7 '18 at 11:45
answered Dec 7 '18 at 11:39
PeterPeter
48.6k1139136
answered Dec 7 '18 at 11:39
PeterPeter
48.6k1139136
answered Dec 7 '18 at 11:39
PeterPeter
48.6k1139136
48.6k1139136
$begingroup$
For example , $$k=10^{170}+8786356$$ does the job
$endgroup$
– Peter
Dec 7 '18 at 11:56
$begingroup$
I can confirm that it is a (probable) Carmichael number using a Pascal implementation of the algorithm from math.stackexchange.com/a/1729144/61216
$endgroup$
– gammatester
Dec 7 '18 at 12:04
$begingroup$
I tested the factors with the APR-test. They are in fact all prime.
$endgroup$
– Peter
Dec 7 '18 at 12:06
$begingroup$
hal.inria.fr/inria-00076980/document could be of interest to you.
$endgroup$
– Claude Leibovici
Dec 7 '18 at 12:25
add a comment |
$begingroup$
For example , $$k=10^{170}+8786356$$ does the job
$endgroup$
– Peter
Dec 7 '18 at 11:56
$begingroup$
I can confirm that it is a (probable) Carmichael number using a Pascal implementation of the algorithm from math.stackexchange.com/a/1729144/61216
$endgroup$
– gammatester
Dec 7 '18 at 12:04
$begingroup$
I tested the factors with the APR-test. They are in fact all prime.
$endgroup$
– Peter
Dec 7 '18 at 12:06
$begingroup$
hal.inria.fr/inria-00076980/document could be of interest to you.
$endgroup$
– Claude Leibovici
Dec 7 '18 at 12:25
$begingroup$
For example , $$k=10^{170}+8786356$$ does the job
$endgroup$
– Peter
Dec 7 '18 at 11:56
$begingroup$
For example , $$k=10^{170}+8786356$$ does the job
$endgroup$
– Peter
Dec 7 '18 at 11:56
$begingroup$
I can confirm that it is a (probable) Carmichael number using a Pascal implementation of the algorithm from math.stackexchange.com/a/1729144/61216
$endgroup$
– gammatester
Dec 7 '18 at 12:04
$begingroup$
I can confirm that it is a (probable) Carmichael number using a Pascal implementation of the algorithm from math.stackexchange.com/a/1729144/61216
$endgroup$
– gammatester
Dec 7 '18 at 12:04
$begingroup$
I tested the factors with the APR-test. They are in fact all prime.
$endgroup$
– Peter
Dec 7 '18 at 12:06
$begingroup$
I tested the factors with the APR-test. They are in fact all prime.
$endgroup$
– Peter
Dec 7 '18 at 12:06
$begingroup$
hal.inria.fr/inria-00076980/document could be of interest to you.
$endgroup$
– Claude Leibovici
Dec 7 '18 at 12:25
$begingroup$
hal.inria.fr/inria-00076980/document could be of interest to you.
$endgroup$
– Claude Leibovici
Dec 7 '18 at 12:25
add a comment |
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