Do we know a $2^{M_i}-1$ that's not prime?
$begingroup$
Do we know a $2^{M_i}-1$ that's composite, i.e. not prime, where $M_i$ is a Mersenne prime number of the form $2^p-1$?
For example
$2^7-1=127$ is not an example because 127 is actually prime.
$2^{11}-1 = 2047 = 23*89$ is not an example because $11$ is not a Mersenne prime ($2^p-1$).
mersenne-numbers
asked Nov 26 '18 at 13:15
Albert HendriksAlbert Hendriks
1919
$endgroup$
add a comment |
$begingroup$
Do we know a $2^{M_i}-1$ that's composite, i.e. not prime, where $M_i$ is a Mersenne prime number of the form $2^p-1$?
For example
$2^7-1=127$ is not an example because 127 is actually prime.
$2^{11}-1 = 2047 = 23*89$ is not an example because $11$ is not a Mersenne prime ($2^p-1$).
mersenne-numbers
asked Nov 26 '18 at 13:15
Albert HendriksAlbert Hendriks
1919
$endgroup$
4
$begingroup$
$2^{8191}-1$ is composite, though $8191=M_{13}$ is a Mersenne prime.
$endgroup$
– lulu
Nov 26 '18 at 13:18
6
$begingroup$
here is the sequence of Mersenne exponents. here is the sequence of Mersenne primes.
$endgroup$
– lulu
Nov 26 '18 at 13:20
add a comment |
$begingroup$
Do we know a $2^{M_i}-1$ that's composite, i.e. not prime, where $M_i$ is a Mersenne prime number of the form $2^p-1$?
For example
$2^7-1=127$ is not an example because 127 is actually prime.
$2^{11}-1 = 2047 = 23*89$ is not an example because $11$ is not a Mersenne prime ($2^p-1$).
mersenne-numbers
asked Nov 26 '18 at 13:15
Albert HendriksAlbert Hendriks
1919
$endgroup$
Do we know a $2^{M_i}-1$ that's composite, i.e. not prime, where $M_i$ is a Mersenne prime number of the form $2^p-1$?
For example
$2^7-1=127$ is not an example because 127 is actually prime.
$2^{11}-1 = 2047 = 23*89$ is not an example because $11$ is not a Mersenne prime ($2^p-1$).
mersenne-numbers
mersenne-numbers
asked Nov 26 '18 at 13:15
Albert HendriksAlbert Hendriks
1919
asked Nov 26 '18 at 13:15
Albert HendriksAlbert Hendriks
1919
asked Nov 26 '18 at 13:15
Albert HendriksAlbert Hendriks
1919
asked Nov 26 '18 at 13:15
Albert HendriksAlbert Hendriks
1919
asked Nov 26 '18 at 13:15
Albert HendriksAlbert Hendriks
1919
1919
4
$begingroup$
$2^{8191}-1$ is composite, though $8191=M_{13}$ is a Mersenne prime.
$endgroup$
– lulu
Nov 26 '18 at 13:18
6
$begingroup$
here is the sequence of Mersenne exponents. here is the sequence of Mersenne primes.
$endgroup$
– lulu
Nov 26 '18 at 13:20
add a comment |
4
$begingroup$
$2^{8191}-1$ is composite, though $8191=M_{13}$ is a Mersenne prime.
$endgroup$
– lulu
Nov 26 '18 at 13:18
6
$begingroup$
here is the sequence of Mersenne exponents. here is the sequence of Mersenne primes.
$endgroup$
– lulu
Nov 26 '18 at 13:20
4
4
$begingroup$
$2^{8191}-1$ is composite, though $8191=M_{13}$ is a Mersenne prime.
$endgroup$
– lulu
Nov 26 '18 at 13:18
$begingroup$
$2^{8191}-1$ is composite, though $8191=M_{13}$ is a Mersenne prime.
$endgroup$
– lulu
Nov 26 '18 at 13:18
6
6
$begingroup$
here is the sequence of Mersenne exponents. here is the sequence of Mersenne primes.
$endgroup$
– lulu
Nov 26 '18 at 13:20
$begingroup$
here is the sequence of Mersenne exponents. here is the sequence of Mersenne primes.
$endgroup$
– lulu
Nov 26 '18 at 13:20
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
As remarked in the comments: $M_{13}=8191$ is the smallest Mersenne Prime which is not also a Mersenne exponent.
Of course, the size of the numbers involved makes it difficult to compute much directly. Still, the available lists are adequate to the purpose at hand. The Mersenne primes are sequence A000668 on OEIS, and the Mersenne exponents are A000043.
answered Nov 26 '18 at 14:35
lulululu
39.8k24778
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3014319%2fdo-we-know-a-2m-i-1-thats-not-prime%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
As remarked in the comments: $M_{13}=8191$ is the smallest Mersenne Prime which is not also a Mersenne exponent.
Of course, the size of the numbers involved makes it difficult to compute much directly. Still, the available lists are adequate to the purpose at hand. The Mersenne primes are sequence A000668 on OEIS, and the Mersenne exponents are A000043.
answered Nov 26 '18 at 14:35
lulululu
39.8k24778
$endgroup$
add a comment |
$begingroup$
As remarked in the comments: $M_{13}=8191$ is the smallest Mersenne Prime which is not also a Mersenne exponent.
Of course, the size of the numbers involved makes it difficult to compute much directly. Still, the available lists are adequate to the purpose at hand. The Mersenne primes are sequence A000668 on OEIS, and the Mersenne exponents are A000043.
answered Nov 26 '18 at 14:35
lulululu
39.8k24778
$endgroup$
add a comment |
$begingroup$
As remarked in the comments: $M_{13}=8191$ is the smallest Mersenne Prime which is not also a Mersenne exponent.
Of course, the size of the numbers involved makes it difficult to compute much directly. Still, the available lists are adequate to the purpose at hand. The Mersenne primes are sequence A000668 on OEIS, and the Mersenne exponents are A000043.
answered Nov 26 '18 at 14:35
lulululu
39.8k24778
$endgroup$
As remarked in the comments: $M_{13}=8191$ is the smallest Mersenne Prime which is not also a Mersenne exponent.
Of course, the size of the numbers involved makes it difficult to compute much directly. Still, the available lists are adequate to the purpose at hand. The Mersenne primes are sequence A000668 on OEIS, and the Mersenne exponents are A000043.
answered Nov 26 '18 at 14:35
lulululu
39.8k24778
answered Nov 26 '18 at 14:35
lulululu
39.8k24778
answered Nov 26 '18 at 14:35
lulululu
39.8k24778
answered Nov 26 '18 at 14:35
lulululu
39.8k24778
39.8k24778
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3014319%2fdo-we-know-a-2m-i-1-thats-not-prime%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
4
$begingroup$
$2^{8191}-1$ is composite, though $8191=M_{13}$ is a Mersenne prime.
$endgroup$
– lulu
Nov 26 '18 at 13:18
6
$begingroup$
here is the sequence of Mersenne exponents. here is the sequence of Mersenne primes.
$endgroup$
– lulu
Nov 26 '18 at 13:20