An iteration produces all the prime numbers

[EdS2]

This very much appeals to me: initially it's rather a surprise.

Take the number 2.920050977316134712092562917112019... and perform the following iteration:
x := IP(x)*FP(x)+IP(x)

(Where IP is the integer part and FP the fractional part.)

Note the integer parts of the resulting sequence!

Ref: this paper or this video or this wikipedia section or this OEIS page.