A conjecture about number 641 The 2019 Stack Overflow Developer Survey Results Are InWeak version of Fortune's conjectureA different approach to the strong Goldbach conjecture?Proof of Prime Maker ConjectureSome questions about Goldbach's conjectureIs my conjecture true? : Every primorial is a superior highly regular number, and every superior highly regular number is a primorial.Is 641 the Smallest Factor of any Composite Fermat Number?Is every primorial number squarefree?Conjecture concerning modular arithmeticConjecture about the prime number functionExpected size of the maximal prime gap below x under Hardy-Littlewood conjecture
Can distinct morphisms between curves induce the same morphism on singular cohomology?
What does "rabbited" mean/imply in this sentence?
Monty Hall variation
In microwave frequencies, do you use a circulator when you need a (near) perfect diode?
What effect does the “loading” weapon property have in practical terms?
Dual Citizen. Exited the US on Italian passport recently
Why is the maximum length of OpenWrt’s root password 8 characters?
What does Linus Torvalds mean when he says that Git "never ever" tracks a file?
How to reverse every other sublist of a list?
On the insanity of kings as an argument against monarchy
CiviEvent: Public link for events of a specific type
Geography at the pixel level
How long do I have to send payment?
Inflated grade on resume at previous job, might former employer tell new employer?
Does it makes sense to buy a new cycle to learn riding?
What can other administrators access on my machine?
Manuscript was "unsubmitted" because the manuscript was deposited in Arxiv Preprints
What is the steepest angle that a canal can be traversable without locks?
Why can Shazam do this?
How are circuits which use complex ICs normally simulated?
JSON.serialize: is it possible to suppress null values of a map?
Falsification in Math vs Science
Are USB sockets on wall outlets live all the time, even when the switch is off?
Why Did Howard Stark Use All The Vibranium They Had On A Prototype Shield?
A conjecture about number 641
The 2019 Stack Overflow Developer Survey Results Are InWeak version of Fortune's conjectureA different approach to the strong Goldbach conjecture?Proof of Prime Maker ConjectureSome questions about Goldbach's conjectureIs my conjecture true? : Every primorial is a superior highly regular number, and every superior highly regular number is a primorial.Is 641 the Smallest Factor of any Composite Fermat Number?Is every primorial number squarefree?Conjecture concerning modular arithmeticConjecture about the prime number functionExpected size of the maximal prime gap below x under Hardy-Littlewood conjecture
$begingroup$
I conjecture that $233#-1$ is the only number of the form $p#-1$, where p is a prime and # denotes the primorial function, which is divisibile by $641$. $641$ is the smallest prime dividing $F_5$, as shown by Euler.
number-theory
asked Mar 30 at 11:37
homunculushomunculus
17410
$endgroup$
add a comment |
$begingroup$
I conjecture that $233#-1$ is the only number of the form $p#-1$, where p is a prime and # denotes the primorial function, which is divisibile by $641$. $641$ is the smallest prime dividing $F_5$, as shown by Euler.
number-theory
asked Mar 30 at 11:37
homunculushomunculus
17410
$endgroup$
$begingroup$
@Peter could you disproof the conjecture?
$endgroup$
– homunculus
Mar 30 at 11:41
2
$begingroup$
The only thing I see about $641$ is that it's prime and it's a factor of $F5$, the 5th Fermat's number. If that's the case, I am not really sure why this type of conjecture should be unique to $641$, if it is indeed true.
$endgroup$
– Mann
Mar 30 at 11:47
$begingroup$
@Mann can you find another prime p such that p#-1 is divisibile by 641?
$endgroup$
– homunculus
Mar 30 at 11:50
$begingroup$
No, what I mean is. What is unique about the conjecture $p' # - 1$ divisible by some prime $p_0$. If it's for $641$, can't I take some other values? What makes you think $641$ and $233$ are unique? This could help us proceed.
$endgroup$
– Mann
Mar 30 at 11:52
add a comment |
$begingroup$
I conjecture that $233#-1$ is the only number of the form $p#-1$, where p is a prime and # denotes the primorial function, which is divisibile by $641$. $641$ is the smallest prime dividing $F_5$, as shown by Euler.
number-theory
asked Mar 30 at 11:37
homunculushomunculus
17410
$endgroup$
I conjecture that $233#-1$ is the only number of the form $p#-1$, where p is a prime and # denotes the primorial function, which is divisibile by $641$. $641$ is the smallest prime dividing $F_5$, as shown by Euler.
number-theory
number-theory
asked Mar 30 at 11:37
homunculushomunculus
17410
asked Mar 30 at 11:37
homunculushomunculus
17410
edited Mar 30 at 12:02
homunculus
asked Mar 30 at 11:37
homunculushomunculus
17410
asked Mar 30 at 11:37
homunculushomunculus
17410
asked Mar 30 at 11:37
homunculushomunculus
17410
17410
$begingroup$
@Peter could you disproof the conjecture?
$endgroup$
– homunculus
Mar 30 at 11:41
2
$begingroup$
The only thing I see about $641$ is that it's prime and it's a factor of $F5$, the 5th Fermat's number. If that's the case, I am not really sure why this type of conjecture should be unique to $641$, if it is indeed true.
$endgroup$
– Mann
Mar 30 at 11:47
$begingroup$
@Mann can you find another prime p such that p#-1 is divisibile by 641?
$endgroup$
– homunculus
Mar 30 at 11:50
$begingroup$
No, what I mean is. What is unique about the conjecture $p' # - 1$ divisible by some prime $p_0$. If it's for $641$, can't I take some other values? What makes you think $641$ and $233$ are unique? This could help us proceed.
$endgroup$
– Mann
Mar 30 at 11:52
add a comment |
$begingroup$
@Peter could you disproof the conjecture?
$endgroup$
– homunculus
Mar 30 at 11:41
2
$begingroup$
The only thing I see about $641$ is that it's prime and it's a factor of $F5$, the 5th Fermat's number. If that's the case, I am not really sure why this type of conjecture should be unique to $641$, if it is indeed true.
$endgroup$
– Mann
Mar 30 at 11:47
$begingroup$
@Mann can you find another prime p such that p#-1 is divisibile by 641?
$endgroup$
– homunculus
Mar 30 at 11:50
$begingroup$
No, what I mean is. What is unique about the conjecture $p' # - 1$ divisible by some prime $p_0$. If it's for $641$, can't I take some other values? What makes you think $641$ and $233$ are unique? This could help us proceed.
$endgroup$
– Mann
Mar 30 at 11:52
$begingroup$
@Peter could you disproof the conjecture?
$endgroup$
– homunculus
Mar 30 at 11:41
$begingroup$
@Peter could you disproof the conjecture?
$endgroup$
– homunculus
Mar 30 at 11:41
2
2
$begingroup$
The only thing I see about $641$ is that it's prime and it's a factor of $F5$, the 5th Fermat's number. If that's the case, I am not really sure why this type of conjecture should be unique to $641$, if it is indeed true.
$endgroup$
– Mann
Mar 30 at 11:47
$begingroup$
The only thing I see about $641$ is that it's prime and it's a factor of $F5$, the 5th Fermat's number. If that's the case, I am not really sure why this type of conjecture should be unique to $641$, if it is indeed true.
$endgroup$
– Mann
Mar 30 at 11:47
$begingroup$
@Mann can you find another prime p such that p#-1 is divisibile by 641?
$endgroup$
– homunculus
Mar 30 at 11:50
$begingroup$
@Mann can you find another prime p such that p#-1 is divisibile by 641?
$endgroup$
– homunculus
Mar 30 at 11:50
$begingroup$
No, what I mean is. What is unique about the conjecture $p' # - 1$ divisible by some prime $p_0$. If it's for $641$, can't I take some other values? What makes you think $641$ and $233$ are unique? This could help us proceed.
$endgroup$
– Mann
Mar 30 at 11:52
$begingroup$
No, what I mean is. What is unique about the conjecture $p' # - 1$ divisible by some prime $p_0$. If it's for $641$, can't I take some other values? What makes you think $641$ and $233$ are unique? This could help us proceed.
$endgroup$
– Mann
Mar 30 at 11:52
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
It is true, but I doubt there's any significance to it. The number $p# - 1$ is clearly not divisible by $641$ if $pgeq 641$, and it turns out that $233# equiv 1pmod641$. Similarly, $3#1 - 1 = 5$ is divisible by $5$; and $7#-1 = 209$ is divisible by $11$ and $19$; and etc.
answered Mar 30 at 12:28
anomalyanomaly
17.8k42666
$endgroup$
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%2f3168204%2fa-conjecture-about-number-641%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
$begingroup$
It is true, but I doubt there's any significance to it. The number $p# - 1$ is clearly not divisible by $641$ if $pgeq 641$, and it turns out that $233# equiv 1pmod641$. Similarly, $3#1 - 1 = 5$ is divisible by $5$; and $7#-1 = 209$ is divisible by $11$ and $19$; and etc.
answered Mar 30 at 12:28
anomalyanomaly
17.8k42666
$endgroup$
add a comment |
$begingroup$
It is true, but I doubt there's any significance to it. The number $p# - 1$ is clearly not divisible by $641$ if $pgeq 641$, and it turns out that $233# equiv 1pmod641$. Similarly, $3#1 - 1 = 5$ is divisible by $5$; and $7#-1 = 209$ is divisible by $11$ and $19$; and etc.
answered Mar 30 at 12:28
anomalyanomaly
17.8k42666
$endgroup$
add a comment |
$begingroup$
It is true, but I doubt there's any significance to it. The number $p# - 1$ is clearly not divisible by $641$ if $pgeq 641$, and it turns out that $233# equiv 1pmod641$. Similarly, $3#1 - 1 = 5$ is divisible by $5$; and $7#-1 = 209$ is divisible by $11$ and $19$; and etc.
answered Mar 30 at 12:28
anomalyanomaly
17.8k42666
$endgroup$
It is true, but I doubt there's any significance to it. The number $p# - 1$ is clearly not divisible by $641$ if $pgeq 641$, and it turns out that $233# equiv 1pmod641$. Similarly, $3#1 - 1 = 5$ is divisible by $5$; and $7#-1 = 209$ is divisible by $11$ and $19$; and etc.
answered Mar 30 at 12:28
anomalyanomaly
17.8k42666
answered Mar 30 at 12:28
anomalyanomaly
17.8k42666
answered Mar 30 at 12:28
anomalyanomaly
17.8k42666
answered Mar 30 at 12:28
anomalyanomaly
17.8k42666
17.8k42666
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%2f3168204%2fa-conjecture-about-number-641%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
$begingroup$
@Peter could you disproof the conjecture?
$endgroup$
– homunculus
Mar 30 at 11:41
2
$begingroup$
The only thing I see about $641$ is that it's prime and it's a factor of $F5$, the 5th Fermat's number. If that's the case, I am not really sure why this type of conjecture should be unique to $641$, if it is indeed true.
$endgroup$
– Mann
Mar 30 at 11:47
$begingroup$
@Mann can you find another prime p such that p#-1 is divisibile by 641?
$endgroup$
– homunculus
Mar 30 at 11:50
$begingroup$
No, what I mean is. What is unique about the conjecture $p' # - 1$ divisible by some prime $p_0$. If it's for $641$, can't I take some other values? What makes you think $641$ and $233$ are unique? This could help us proceed.
$endgroup$
– Mann
Mar 30 at 11:52