Let Sm(n)=$1234567891011...$n.Numbers from concatenating the first n natural numbers ($123456789...$n)is also called a Smarandache number. And now consider this sequence: numbers n greater than one, such that Sm(n) create a new record for larger least prime divisor for all $1<m<=n$. The sequence begins, n=$2$,$3$,$7$,$61$,$121$,$133$...,with the corresponding least prime divisors of $2$,$3$,$127$,$10386763$,$278240783$,$8223519074965787731$. What is the next term after $133$ ?. I've checked Fleuren(?)'s factorizations of Smarandache numbers Sm(n), and other sites but I couldn't find the next term after $133$. I couldn't find the next term myself because of factoring problem,but I'm quite sure that the next term is greater than $319$. Can you find the next term(s) after $133$ ?

  • $\begingroup$ Link. $\endgroup$ – Lucian Nov 17 '15 at 18:16
  • $\begingroup$ @Lucian, that site has a limit for the number of digits. $\endgroup$ – Takuma Sannz Nov 17 '15 at 18:31

The next term is $133$ with the least prime divisor of $8 223 519 074 965 787 731$. And the next term after $133$ is greater than 319

  • $\begingroup$ Please use the edit link on your question to add additional information. The Post Answer button should be used only for complete answers to the question. - From Review $\endgroup$ – Alex M. Nov 17 '15 at 17:55
  • $\begingroup$ @AlexM.I didn't intentionally do that, I really just got that answer 133,and the next term after 133 will have least prime factor with 19 digits or (much) more (!) $\endgroup$ – Takuma Sannz Nov 17 '15 at 18:01
  • $\begingroup$ @AlexM.What do you mean with compete answers ?,this question is clearly very hard to answer. We are lucky if we can find the next 2 or 3 terms after 121 $\endgroup$ – Takuma Sannz Nov 17 '15 at 18:17
  • $\begingroup$ This was not written by me myself, it is text automatically generated by the software of MSE. $\endgroup$ – Alex M. Nov 17 '15 at 18:22
  • $\begingroup$ How I can delete my own answer ?. I don't know how.Can someone delete this ? $\endgroup$ – Takuma Sannz Nov 17 '15 at 18:24

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