Are Mersenne numbers with Mersenne prime exponent always prime?












0












$begingroup$


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







share|cite|improve this question











$endgroup$












  • $begingroup$
    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


















0












$begingroup$


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







share|cite|improve this question











$endgroup$












  • $begingroup$
    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
















0












0








0





$begingroup$


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







share|cite|improve this question











$endgroup$




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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 11 '18 at 14:29









Klangen

1,72811334




1,72811334










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




















  • $begingroup$
    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












2 Answers
2






active

oldest

votes


















1












$begingroup$

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.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Yes. That would be true.
    $endgroup$
    – Harshith Vasireddy
    Oct 15 '18 at 11:22



















1












$begingroup$

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.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    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 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











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2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






active

oldest

votes









1












$begingroup$

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.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Yes. That would be true.
    $endgroup$
    – Harshith Vasireddy
    Oct 15 '18 at 11:22
















1












$begingroup$

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.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Yes. That would be true.
    $endgroup$
    – Harshith Vasireddy
    Oct 15 '18 at 11:22














1












1








1





$begingroup$

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.






share|cite|improve this answer









$endgroup$



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.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










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


















  • $begingroup$
    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











1












$begingroup$

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.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    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 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
















1












$begingroup$

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.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    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 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














1












1








1





$begingroup$

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.






share|cite|improve this answer











$endgroup$



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.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Oct 15 '18 at 11:15

























answered Oct 15 '18 at 11:08









gammatestergammatester

16.7k21633




16.7k21633












  • $begingroup$
    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












  • $begingroup$
    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










  • $begingroup$
    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
















$begingroup$
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


















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