# Another Note on the Greatest Prime Factors of Fermat Numbers

```@article{Grytczuk2001AnotherNO,
title={Another Note on the Greatest Prime Factors of Fermat Numbers},
author={Aleksander Grytczuk and Marek W{\'o}jtowicz and Florian Luca},
journal={Southeast Asian Bulletin of Mathematics},
year={2001},
volume={25},
pages={111-115}
}```
• Published 1 July 2001
• Mathematics
• Southeast Asian Bulletin of Mathematics
For every positive integer k > 1, let P(k) be the largest prime divisor of k. In this note, we show that if Fm = 22m + 1 is the m‘th Fermat number, then P(Fm) ≥ 2m+2(4m + 9) + 1 for all m ≥ 4. We also give a lower bound of a similar type for P(Fa,m), where Fa,m = a2m + 1 whenever a is even and m ≥ a18.
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## References

On the large sieve
The purpose of this paper is to give a new and improved version of Linnik's large sieve, with some applications. The large sieve has its roots in the Hardy-Littlewood method, and in its most general