## Odd perfect numbers have a prime factor exceeding $10^8$

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- by Takeshi Goto and Yasuo Ohno PDF
- Math. Comp.
**77**(2008), 1859-1868 Request permission

## Abstract:

Jenkins in 2003 showed that every odd perfect number is divisible by a prime exceeding $10^7$. Using the properties of cyclotomic polynomials, we improve this result to show that every perfect number is divisible by a prime exceeding $10^8$.## References

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## Additional Information

**Takeshi Goto**- Affiliation: Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba, 278-8510, Japan
- Email: goto_takeshi@ma.noda.tus.ac.jp
**Yasuo Ohno**- Affiliation: Department of Mathematics, Kinki University Higashi-Osaka, Osaka 577-8502, Japan
- Email: ohno@math.kindai.ac.jp
- Received by editor(s): December 13, 2006
- Received by editor(s) in revised form: February 26, 2007
- Published electronically: February 12, 2008
- Additional Notes: This work was supported by Computing and Communications Center, Kyushu University

The second author was supported in part by JSPS Grant-in-Aid No. 15740025 and No. 18740020 - © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp.
**77**(2008), 1859-1868 - MSC (2000): Primary 11A25, 11Y70
- DOI: https://doi.org/10.1090/S0025-5718-08-02050-4
- MathSciNet review: 2398799