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  • $\begingroup$ Any prime number where $1$ appears as a digit exactly once will work. $\endgroup$ Commented Jan 26, 2021 at 19:15
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    $\begingroup$ @user44191 sorry, I should have emphasized the composite number part of the conjectures $\endgroup$ Commented Jan 26, 2021 at 21:11
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    $\begingroup$ Thinking about it a bit, I believe that a composite number can have at most the same number of digits as its prime factors combined, so the multiset of the digits of the number would have to be equal to the multiset of the digits of all the prime factors. i.e. you can't have a bigger or smaller number of digits in the number than you have in the combined prime factors. Don't know if that helps at all. $\endgroup$ Commented Jan 28, 2021 at 17:33
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    $\begingroup$ If you're interested in the substring, rather than subsequence, version where repeats are allowed, it's oeis.org/A050694 $\endgroup$ Commented Jan 29, 2021 at 3:45
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    $\begingroup$ Checking up to 2^31 still reveals no solutions. $\endgroup$ Commented Sep 18, 2022 at 15:58