随便选的
https://en.wikipedia.org/wiki/65,537

65537 is commonly used as a public exponent in the RSA cryptosystem. Because it is the Fermat number Fn = 22n + 1 with n = 4, the common shorthand is "F4" or "F4".[3] This value was used in RSA mainly for historical reasons; early raw RSA implementations (without proper padding) were vulnerable to very small exponents, while use of high exponents was computationally expensive with no advantage to security (assuming proper padding).[4]

不懂，我以为就是随便选了个质数。
看看这里，也许有帮助。

https://en.wikipedia.org/wiki/RSA_(cryptosystem)

e having a short bit-length and small Hamming weight results in more efficient encryption – the most commonly chosen value for e is 216 + 1 = 65537. The smallest (and fastest) possible value for e is 3, but such a small value for e has been shown to be less secure in some settings.

@rabbbit 哎，不仅数学不会，English 还不懂，咱果然不适合研究这么深奥的学问。

看了半天，我的理解是，一个小于 φn 且是相对小的数。
但是不知道这是不是正确的理解。

，
𝑝
=
11
p=11 和
𝑞
=
19
q=19 ，所以：

𝜙
(
𝑛
)
=
(
𝑝
−
1
)
(
𝑞
−
1
)
=
(
11
−
1
)
(
19
−
1
)
=
10
×
18
=
180
ϕ(n)=(p−1)(q−1)=(11−1)(19−1)=10×18=180