Expect at Most One Billionth of a New Fermat Prime!

@article{Boklan2016ExpectAM,
  title={Expect at Most One Billionth of a New Fermat Prime!},
  author={Kent D. Boklan and John H. Conway},
  journal={The Mathematical Intelligencer},
  year={2016},
  volume={39},
  pages={3-5}
}
We provide compelling evidence that all Fermat primes were already known to Fermat. 
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4 Citations

4 Citations

Why Does a Prime p Divide a Fermat Number?
Summary A prime dividing a composite Fermat number is called a Fermat prime divisor. Such a prime p must be congruent to 1 modulo 4, and so, by the Fermat–Girard theorem, there exists integers R and…
6m Theorem for Prime numbers
We show that for any $P= 6^{m+1}.N -1 $ is a prime number for any $1 13 $ if and only if , $N \ne i^{m+1}Mod(6i+1) +(6i +1)a $ $ ; i,a \le Z^+ $
BiEntropy, TriEntropy and Primality
TLDR
A significant relationship between BiEntropy and TriEntropy is found such that the twin primes conjecture is true and the BiEntropic prime density is shown to be quadratic with a very small Gaussian distributed error.
Frobenius Groups with Perfect Order Classes
The purpose of this paper is to investigate the finite Frobenius groups with “perfect order classes”; that is, those for which the number of elements of each order is a divisor of the order of the…

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TLDR
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Expect at most one billionth of a new Fermat Prime
  • 2016