Are Mersenne numbers with Mersenne prime exponent always prime?
$begingroup$
A Mersenne number is a number on the form $2^n-1$. For it to be prime, the number $n$ must be prime. My question is that if $n$ is another Mersenne prime, will $2^n-1$ be always prime?
It seems so, to me anyway.
prime-numbers mersenne-numbers
edited Dec 11 '18 at 14:29
Klangen
1,75811334
asked Oct 15 '18 at 10:46
Harshith VasireddyHarshith Vasireddy
12
$endgroup$
add a comment |
$begingroup$
A Mersenne number is a number on the form $2^n-1$. For it to be prime, the number $n$ must be prime. My question is that if $n$ is another Mersenne prime, will $2^n-1$ be always prime?
It seems so, to me anyway.
prime-numbers mersenne-numbers
edited Dec 11 '18 at 14:29
Klangen
1,75811334
asked Oct 15 '18 at 10:46
Harshith VasireddyHarshith Vasireddy
12
$endgroup$
$begingroup$
If this were true, this would generate info itelyinfjnitely many mersenne primes! We currently know of only 48.
$endgroup$
– JavaMan
Oct 15 '18 at 10:50
add a comment |
$begingroup$
A Mersenne number is a number on the form $2^n-1$. For it to be prime, the number $n$ must be prime. My question is that if $n$ is another Mersenne prime, will $2^n-1$ be always prime?
It seems so, to me anyway.
prime-numbers mersenne-numbers
edited Dec 11 '18 at 14:29
Klangen
1,75811334
asked Oct 15 '18 at 10:46
Harshith VasireddyHarshith Vasireddy
12
$endgroup$
A Mersenne number is a number on the form $2^n-1$. For it to be prime, the number $n$ must be prime. My question is that if $n$ is another Mersenne prime, will $2^n-1$ be always prime?
It seems so, to me anyway.
prime-numbers mersenne-numbers
prime-numbers mersenne-numbers
edited Dec 11 '18 at 14:29
Klangen
1,75811334
asked Oct 15 '18 at 10:46
Harshith VasireddyHarshith Vasireddy
12
edited Dec 11 '18 at 14:29
Klangen
1,75811334
asked Oct 15 '18 at 10:46
Harshith VasireddyHarshith Vasireddy
12
edited Dec 11 '18 at 14:29
Klangen
1,75811334
edited Dec 11 '18 at 14:29
Klangen
1,75811334
edited Dec 11 '18 at 14:29
Klangen
1,75811334
1,75811334
asked Oct 15 '18 at 10:46
Harshith VasireddyHarshith Vasireddy
12
asked Oct 15 '18 at 10:46
Harshith VasireddyHarshith Vasireddy
12
asked Oct 15 '18 at 10:46
Harshith VasireddyHarshith Vasireddy
12
12
$begingroup$
If this were true, this would generate info itelyinfjnitely many mersenne primes! We currently know of only 48.
$endgroup$
– JavaMan
Oct 15 '18 at 10:50
add a comment |
$begingroup$
If this were true, this would generate info itelyinfjnitely many mersenne primes! We currently know of only 48.
$endgroup$
– JavaMan
Oct 15 '18 at 10:50
$begingroup$
If this were true, this would generate info itelyinfjnitely many mersenne primes! We currently know of only 48.
$endgroup$
– JavaMan
Oct 15 '18 at 10:50
$begingroup$
If this were true, this would generate info itelyinfjnitely many mersenne primes! We currently know of only 48.
$endgroup$
– JavaMan
Oct 15 '18 at 10:50
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
https://oeis.org/A000043
We only know about finitely many Mersenne primes. If your conjecture was true, then we could generate infinitely many Mersenne primes.
answered Oct 15 '18 at 11:10
math783625math783625
31210
$endgroup$
$begingroup$
Yes. That would be true.
$endgroup$
– Harshith Vasireddy
Oct 15 '18 at 11:22
add a comment |
$begingroup$
My own program found that $2^{2^{13} - 1} - 1$ is not a (probable) prime number, confirmed by Wolfram Alpha and https://oeis.org/A000043. Note that $M_{13} = 8191$ is prime and $M_{8191}$ is not.
answered Oct 15 '18 at 11:08
gammatestergammatester
16.7k21733
$endgroup$
$begingroup$
Wolfram alpha says result unknown
$endgroup$
– Harshith Vasireddy
Oct 15 '18 at 11:21
$begingroup$
For me is says it is not (after a few seconds), query wasisprime 2^(2^13-1)-1. Anyway, $M_{8191}$ is not in the list of Mersenne primes.
$endgroup$
– gammatester
Oct 15 '18 at 11:23
$begingroup$
Thanks. Doubt clarified
$endgroup$
– Harshith Vasireddy
Oct 15 '18 at 11:29
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
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active
oldest
votes
$begingroup$
https://oeis.org/A000043
We only know about finitely many Mersenne primes. If your conjecture was true, then we could generate infinitely many Mersenne primes.
answered Oct 15 '18 at 11:10
math783625math783625
31210
$endgroup$
$begingroup$
Yes. That would be true.
$endgroup$
– Harshith Vasireddy
Oct 15 '18 at 11:22
add a comment |
$begingroup$
https://oeis.org/A000043
We only know about finitely many Mersenne primes. If your conjecture was true, then we could generate infinitely many Mersenne primes.
answered Oct 15 '18 at 11:10
math783625math783625
31210
$endgroup$
$begingroup$
Yes. That would be true.
$endgroup$
– Harshith Vasireddy
Oct 15 '18 at 11:22
add a comment |
$begingroup$
https://oeis.org/A000043
We only know about finitely many Mersenne primes. If your conjecture was true, then we could generate infinitely many Mersenne primes.
answered Oct 15 '18 at 11:10
math783625math783625
31210
$endgroup$
https://oeis.org/A000043
We only know about finitely many Mersenne primes. If your conjecture was true, then we could generate infinitely many Mersenne primes.
answered Oct 15 '18 at 11:10
math783625math783625
31210
answered Oct 15 '18 at 11:10
math783625math783625
31210
answered Oct 15 '18 at 11:10
math783625math783625
31210
answered Oct 15 '18 at 11:10
math783625math783625
31210
31210
$begingroup$
Yes. That would be true.
$endgroup$
– Harshith Vasireddy
Oct 15 '18 at 11:22
add a comment |
$begingroup$
Yes. That would be true.
$endgroup$
– Harshith Vasireddy
Oct 15 '18 at 11:22
$begingroup$
Yes. That would be true.
$endgroup$
– Harshith Vasireddy
Oct 15 '18 at 11:22
$begingroup$
Yes. That would be true.
$endgroup$
– Harshith Vasireddy
Oct 15 '18 at 11:22
add a comment |
$begingroup$
My own program found that $2^{2^{13} - 1} - 1$ is not a (probable) prime number, confirmed by Wolfram Alpha and https://oeis.org/A000043. Note that $M_{13} = 8191$ is prime and $M_{8191}$ is not.
answered Oct 15 '18 at 11:08
gammatestergammatester
16.7k21733
$endgroup$
$begingroup$
Wolfram alpha says result unknown
$endgroup$
– Harshith Vasireddy
Oct 15 '18 at 11:21
$begingroup$
For me is says it is not (after a few seconds), query wasisprime 2^(2^13-1)-1. Anyway, $M_{8191}$ is not in the list of Mersenne primes.
$endgroup$
– gammatester
Oct 15 '18 at 11:23
$begingroup$
Thanks. Doubt clarified
$endgroup$
– Harshith Vasireddy
Oct 15 '18 at 11:29
add a comment |
$begingroup$
My own program found that $2^{2^{13} - 1} - 1$ is not a (probable) prime number, confirmed by Wolfram Alpha and https://oeis.org/A000043. Note that $M_{13} = 8191$ is prime and $M_{8191}$ is not.
answered Oct 15 '18 at 11:08
gammatestergammatester
16.7k21733
$endgroup$
$begingroup$
Wolfram alpha says result unknown
$endgroup$
– Harshith Vasireddy
Oct 15 '18 at 11:21
$begingroup$
For me is says it is not (after a few seconds), query wasisprime 2^(2^13-1)-1. Anyway, $M_{8191}$ is not in the list of Mersenne primes.
$endgroup$
– gammatester
Oct 15 '18 at 11:23
$begingroup$
Thanks. Doubt clarified
$endgroup$
– Harshith Vasireddy
Oct 15 '18 at 11:29
add a comment |
$begingroup$
My own program found that $2^{2^{13} - 1} - 1$ is not a (probable) prime number, confirmed by Wolfram Alpha and https://oeis.org/A000043. Note that $M_{13} = 8191$ is prime and $M_{8191}$ is not.
answered Oct 15 '18 at 11:08
gammatestergammatester
16.7k21733
$endgroup$
My own program found that $2^{2^{13} - 1} - 1$ is not a (probable) prime number, confirmed by Wolfram Alpha and https://oeis.org/A000043. Note that $M_{13} = 8191$ is prime and $M_{8191}$ is not.
answered Oct 15 '18 at 11:08
gammatestergammatester
16.7k21733
edited Oct 15 '18 at 11:15
answered Oct 15 '18 at 11:08
gammatestergammatester
16.7k21733
answered Oct 15 '18 at 11:08
gammatestergammatester
16.7k21733
answered Oct 15 '18 at 11:08
gammatestergammatester
16.7k21733
16.7k21733
$begingroup$
Wolfram alpha says result unknown
$endgroup$
– Harshith Vasireddy
Oct 15 '18 at 11:21
$begingroup$
For me is says it is not (after a few seconds), query wasisprime 2^(2^13-1)-1. Anyway, $M_{8191}$ is not in the list of Mersenne primes.
$endgroup$
– gammatester
Oct 15 '18 at 11:23
$begingroup$
Thanks. Doubt clarified
$endgroup$
– Harshith Vasireddy
Oct 15 '18 at 11:29
add a comment |
$begingroup$
Wolfram alpha says result unknown
$endgroup$
– Harshith Vasireddy
Oct 15 '18 at 11:21
$begingroup$
For me is says it is not (after a few seconds), query wasisprime 2^(2^13-1)-1. Anyway, $M_{8191}$ is not in the list of Mersenne primes.
$endgroup$
– gammatester
Oct 15 '18 at 11:23
$begingroup$
Thanks. Doubt clarified
$endgroup$
– Harshith Vasireddy
Oct 15 '18 at 11:29
$begingroup$
Wolfram alpha says result unknown
$endgroup$
– Harshith Vasireddy
Oct 15 '18 at 11:21
$begingroup$
Wolfram alpha says result unknown
$endgroup$
– Harshith Vasireddy
Oct 15 '18 at 11:21
$begingroup$
For me is says it is not (after a few seconds), query was
isprime 2^(2^13-1)-1. Anyway, $M_{8191}$ is not in the list of Mersenne primes.$endgroup$
– gammatester
Oct 15 '18 at 11:23
$begingroup$
For me is says it is not (after a few seconds), query was
isprime 2^(2^13-1)-1. Anyway, $M_{8191}$ is not in the list of Mersenne primes.$endgroup$
– gammatester
Oct 15 '18 at 11:23
$begingroup$
Thanks. Doubt clarified
$endgroup$
– Harshith Vasireddy
Oct 15 '18 at 11:29
$begingroup$
Thanks. Doubt clarified
$endgroup$
– Harshith Vasireddy
Oct 15 '18 at 11:29
add a comment |
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$begingroup$
If this were true, this would generate info itelyinfjnitely many mersenne primes! We currently know of only 48.
$endgroup$
– JavaMan
Oct 15 '18 at 10:50