Below is a poem due to John M. Pollard, called A Tale of Three Sieves, which he e-mailed to me. Everything that follows (i.e. including the notes) is a direct quote from that e-mail.
Notes. The first verse is not original - I don`t know the author. The title was suggested by that of Pomerance: "A Tale of Two Sieves", Notices of the AMS, December 1996, 1473-1485.
"Sieve the twos and sieve the threes -
The sieve of Eratosthenes!
When the multiples sublime
The numbers which remain are prime!
Add log p as you advance -
Such is the sieve of Pomerance!
The largest sums which you have found
Give numbers which are smooth and round!
Mark out a gigantic square.
Add logs at random everywhere.
This brief account you must forgive
Of Pollard`s Number Field Sieve!"
More notes for beginners:
"I've factored large numbers,
I've factored small,
Sooner or later,
I'll factor them all."
-- Scott Contini