My favorite prime number generator

My favorite prime number generator is

    ┬─┬───────────────────────────────────┬──── ────┬
    │ │ ┬─┬ ────┬─┬────────────────────── ┼───┬ ┬───┼
    │ │ └─┤ ────┼─┼───────────────────┬── ┼───┼ │ ┬ │
    │ │   │ ┬───┼─┼───────────────────┼── ┼─┬─┼ │ ┼ │
    │ │   │ │ ─ ┼─┼─┬─────┬──── ──────┼─┬ │ ├─┘ └─┤ │
    │ │   │ │ ┬ └─┤ │ ┬─┬ ┼─┬─┬ ──┬───┼─┼ ├─┘     ├─┘
    │ │   │ └─┤   └─┤ └─┤ │ ├─┘ ──┼─┬─┼─┼ │       │
    │ │   │   │     │   │ ├─┘   ┬─┼─┼─┼─┼ │       │
    │ │   │   │     │   ├─┘     └─┤ │ ├─┘ │       │
    │ │   │   │     └───┤         │ ├─┘   │       │
    │ │   │   │         │         ├─┘     │       │
    │ │   │   │         ├─────────┘       │       │
    │ │   │   ├─────────┘                 │       │
    │ │   └───┤                           │       │
    │ │       ├───────────────────────────┘       │
    │ ├───────┘                                   │
    └─┤                                           │
      └───────────────────────────────────────────┘

which graphically depicts the 167-bit lambda term

    λ 1 (1 ((λ 1 1) (λ λ λ 1 (λ λ 1) ((λ 4 4 1 ((λ 1 1) (λ 2 (1 1)))) (λ λ λ λ 1 3 (2 (6 4))))) (λ λ λ 4 (1 3)))) (λ λ 1 (λ λ 2) 2)

which generates the characteristic sequence of primes [1] [2].

[1] https://tromp.github.io/cl/cl.html

[2] https://github.com/tromp/AIT/blob/master/characteristic_sequ...

My favourite prime number generator is this one using go channels to create filters. Not efficient but fun.

https://go.dev/play/p/9U22NfrXeq

In J generating prime numbers is simply p:21, that gives you 79 which is the 21st prime number.

It is so fast, I wonder what the algorithm behind it is.

[0]: https://code.jsoftware.com/wiki/Vocabulary/pco

Can I just say how surprised I am the many people have a favourite prime number generator.

I can’t say I have a favourite but I do enjoy multiplying two random prime numbers with each other and using the random result when I need a random number with added random.

The Sieve of Atkin is VERY fast at generating primes between 1 and n.

It asymptotically speeds up the process of generating prime numbers. It has time complexity O(n/(log log n))

https://www.baeldung.com/cs/prime-number-algorithms