Large 2-digit numbers that factor into 2-digit numbers.











up vote
5
down vote

favorite
3












$799777779779979$ and $111111811818111$ are numbers of $2$ non-zero digits that can be factored into $2$-digit numbers. They are $97$-smooth numbers.



Are there any larger examples?










share|cite|improve this question




















  • 1




    "numbers of 2 non-zero digits" means what?
    – Thomas Andrews
    Feb 3 '17 at 22:05






  • 1




    Note that "friable" is a more descriptive and more modern term than the conventional "smooth" in this context.
    – Greg Martin
    Feb 3 '17 at 22:05






  • 1




    According to my calculation, a larger example must have more than $20$ digits. The ratio of smooth numbers decreases drastically , so it is well possible that no larger example exists.
    – Peter
    Feb 4 '17 at 21:53















up vote
5
down vote

favorite
3












$799777779779979$ and $111111811818111$ are numbers of $2$ non-zero digits that can be factored into $2$-digit numbers. They are $97$-smooth numbers.



Are there any larger examples?










share|cite|improve this question




















  • 1




    "numbers of 2 non-zero digits" means what?
    – Thomas Andrews
    Feb 3 '17 at 22:05






  • 1




    Note that "friable" is a more descriptive and more modern term than the conventional "smooth" in this context.
    – Greg Martin
    Feb 3 '17 at 22:05






  • 1




    According to my calculation, a larger example must have more than $20$ digits. The ratio of smooth numbers decreases drastically , so it is well possible that no larger example exists.
    – Peter
    Feb 4 '17 at 21:53













up vote
5
down vote

favorite
3









up vote
5
down vote

favorite
3






3





$799777779779979$ and $111111811818111$ are numbers of $2$ non-zero digits that can be factored into $2$-digit numbers. They are $97$-smooth numbers.



Are there any larger examples?










share|cite|improve this question















$799777779779979$ and $111111811818111$ are numbers of $2$ non-zero digits that can be factored into $2$-digit numbers. They are $97$-smooth numbers.



Are there any larger examples?







combinatorics number-theory recreational-mathematics prime-factorization






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 22 at 12:57









Klangen

1,43711232




1,43711232










asked Feb 3 '17 at 21:49









Ed Pegg

9,73432591




9,73432591








  • 1




    "numbers of 2 non-zero digits" means what?
    – Thomas Andrews
    Feb 3 '17 at 22:05






  • 1




    Note that "friable" is a more descriptive and more modern term than the conventional "smooth" in this context.
    – Greg Martin
    Feb 3 '17 at 22:05






  • 1




    According to my calculation, a larger example must have more than $20$ digits. The ratio of smooth numbers decreases drastically , so it is well possible that no larger example exists.
    – Peter
    Feb 4 '17 at 21:53














  • 1




    "numbers of 2 non-zero digits" means what?
    – Thomas Andrews
    Feb 3 '17 at 22:05






  • 1




    Note that "friable" is a more descriptive and more modern term than the conventional "smooth" in this context.
    – Greg Martin
    Feb 3 '17 at 22:05






  • 1




    According to my calculation, a larger example must have more than $20$ digits. The ratio of smooth numbers decreases drastically , so it is well possible that no larger example exists.
    – Peter
    Feb 4 '17 at 21:53








1




1




"numbers of 2 non-zero digits" means what?
– Thomas Andrews
Feb 3 '17 at 22:05




"numbers of 2 non-zero digits" means what?
– Thomas Andrews
Feb 3 '17 at 22:05




1




1




Note that "friable" is a more descriptive and more modern term than the conventional "smooth" in this context.
– Greg Martin
Feb 3 '17 at 22:05




Note that "friable" is a more descriptive and more modern term than the conventional "smooth" in this context.
– Greg Martin
Feb 3 '17 at 22:05




1




1




According to my calculation, a larger example must have more than $20$ digits. The ratio of smooth numbers decreases drastically , so it is well possible that no larger example exists.
– Peter
Feb 4 '17 at 21:53




According to my calculation, a larger example must have more than $20$ digits. The ratio of smooth numbers decreases drastically , so it is well possible that no larger example exists.
– Peter
Feb 4 '17 at 21:53















active

oldest

votes











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',
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
});


}
});














draft saved

draft discarded


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2128059%2flarge-2-digit-numbers-that-factor-into-2-digit-numbers%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown






























active

oldest

votes













active

oldest

votes









active

oldest

votes






active

oldest

votes
















draft saved

draft discarded




















































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.





Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


Please pay close attention to the following guidance:


  • 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.


To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2128059%2flarge-2-digit-numbers-that-factor-into-2-digit-numbers%23new-answer', 'question_page');
}
);

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







Popular posts from this blog

Ellipse (mathématiques)

Quarter-circle Tiles

Mont Emei