The Wild Number Problem: Math or Fiction?

@article{Schogt2013TheWN,
  title={The Wild Number Problem: Math or Fiction?},
  author={Philibert Schogt},
  journal={arXiv: History and Overview},
  year={2013},
  pages={31-38}
}
In the above scene from my novel The Wild Numbers, the 35-year-old mathematician Isaac Swift believes he has found a solution to the famous Wild Number Problem and is showing it to his older colleague, the Russian mathematician Dimitri Arkanov. But what exactly is the Wild Number Problem, and why did I choose it as the theme for my novel, rather than some other mathematical problem? 

References

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Wild and Wooley Numbers
  • J. Lagarias
  • Mathematics, Computer Science
  • Am. Math. Mon.
  • 2006
TLDR
Evidence that the wild numbers are the set of all prime numbers excluding 3 is presented, and various open problems are formulated about Wooley integers. Expand
The 3x + 1 semigroup
Abstract The 3 x + 1 semigroup is the multiplicative semigroup S of positive rational numbers generated by { 2 k + 1 3 k + 2 : k ⩾ 0 } together with { 2 } . This semigroup encodes backwards iterationExpand
The Wild Numbers