Multi-base primes: Difference between revisions

</pre>

===Up to base 62===

{{trans|C++}}

<lang rust>// [dependencies]

// primal = "0.3"

fn to_string(digits: &[usize]) -> String {

const DIGITS: [char; 62] = [

'0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h',

'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z',

'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R',

'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z',

];

let mut str = String::new();

for d in digits {

str.push(DIGITS[*d]);

}

str

}

fn increment(digits: &mut [usize], base: usize) -> bool {

let mut i = digits.len();

while i > 0 && digits[i - 1] + 1 == base {

digits[i - 1] = 0;

i -= 1;

}

if i == 0 {

return false;

}

digits[i - 1] += 1;

true

}

fn multi_base_primes(max_base: usize, max_length: usize) {

let sieve = primal::Sieve::new(max_base.pow(max_length as u32));

for length in 1..=max_length {

let mut most_bases = 0;

let mut max_strings = Vec::new();

let mut digits = vec![0; length];

digits[0] = 1;

let mut bases = Vec::new();

loop {

let mut min_base = 2;

if let Some(max) = digits.iter().max() {

min_base = std::cmp::max(min_base, max + 1);

}

if most_bases <= max_base - min_base + 1 {

bases.clear();

for b in min_base..=max_base {

if max_base - b + 1 + bases.len() < most_bases {

break;

}

let mut n = 0;

for d in &digits {

n = n * b + d;

}

if sieve.is_prime(n) {

bases.push(b);

}

}

if bases.len() > most_bases {

most_bases = bases.len();

max_strings.clear();

}

if bases.len() == most_bases {

max_strings.push((digits.clone(), bases.clone()));

}

}

if !increment(&mut digits, max_base) {

break;

}

}

println!(

"{}-character strings which are prime in most bases: {}",

length, most_bases

);

for (digits, bases) in max_strings {

println!("{} -> {:?}", to_string(&digits), bases);

}

println!();

}

}

fn main() {

let args: Vec<String> = std::env::args().collect();

let mut max_base = 36;

let mut max_length = 4;

let mut arg = 0;

while arg + 1 < args.len() {

if args[arg] == "-max_base" {

arg += 1;

match args[arg].parse::<usize>() {

Ok(n) => max_base = n,

Err(error) => {

eprintln!("{}", error);

return;

}

}

} else if args[arg] == "-max_length" {

arg += 1;

match args[arg].parse::<usize>() {

Ok(n) => max_length = n,

Err(error) => {

eprintln!("{}", error);

return;

}

}

}

arg += 1;

}

if max_base > 62 {

eprintln!("Maximum base cannot be greater than 62.");

} else if max_base < 2 {

eprintln!("Maximum base cannot be less than 2.");

} else {

use std::time::Instant;

let now = Instant::now();

multi_base_primes(max_base, max_length);

let time = now.elapsed();

println!("elapsed time: {} milliseconds", time.as_millis());

}

}</lang>

{{out}}

CPU: Intel Core i5-4570 3.2GHz.

Maximum base 36, maximum length 6:

<pre>

1-character strings which are prime in most bases: 34

2 -> [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36]

2-character strings which are prime in most bases: 18

21 -> [3, 5, 6, 8, 9, 11, 14, 15, 18, 20, 21, 23, 26, 29, 30, 33, 35, 36]

3-character strings which are prime in most bases: 18

131 -> [4, 5, 7, 8, 9, 10, 12, 14, 15, 18, 19, 20, 23, 25, 27, 29, 30, 34]

551 -> [6, 7, 11, 13, 14, 15, 16, 17, 19, 21, 22, 24, 25, 26, 30, 32, 35, 36]

737 -> [8, 9, 11, 12, 13, 15, 16, 17, 19, 22, 23, 24, 25, 26, 29, 30, 31, 36]

4-character strings which are prime in most bases: 19

1727 -> [8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 22, 23, 24, 26, 27, 29, 31, 33, 36]

5347 -> [8, 9, 10, 11, 12, 13, 16, 18, 19, 22, 24, 25, 26, 30, 31, 32, 33, 34, 36]

5-character strings which are prime in most bases: 18

30271 -> [8, 10, 12, 13, 16, 17, 18, 20, 21, 23, 24, 25, 31, 32, 33, 34, 35, 36]

6-character strings which are prime in most bases: 18

441431 -> [5, 8, 9, 11, 12, 14, 16, 17, 19, 21, 22, 23, 26, 28, 30, 31, 32, 33]

elapsed time: 14783 milliseconds

</pre>

Maximum base 62, maximum length 5:

<pre>

1-character strings which are prime in most bases: 60

2 -> [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62]

2-character strings which are prime in most bases: 31

65 -> [7, 8, 9, 11, 13, 14, 16, 17, 18, 21, 22, 24, 27, 28, 29, 31, 32, 37, 38, 39, 41, 42, 43, 44, 46, 48, 51, 52, 57, 58, 59]

3-character strings which are prime in most bases: 33

1l1 -> [22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 48, 51, 52, 53, 54, 57, 58, 59, 60, 61, 62]

b9b -> [13, 14, 15, 16, 17, 19, 20, 21, 23, 24, 26, 27, 28, 30, 31, 34, 36, 39, 40, 42, 45, 47, 49, 50, 52, 53, 54, 57, 58, 59, 60, 61, 62]

4-character strings which are prime in most bases: 32

1727 -> [8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 22, 23, 24, 26, 27, 29, 31, 33, 36, 37, 38, 39, 41, 45, 46, 48, 50, 51, 57, 58, 60, 61]

417b -> [12, 13, 15, 16, 17, 18, 19, 21, 23, 25, 28, 30, 32, 34, 35, 37, 38, 39, 41, 45, 48, 49, 50, 51, 52, 54, 56, 57, 58, 59, 61, 62]

5-character strings which are prime in most bases: 30

50161 -> [7, 8, 9, 13, 17, 18, 19, 20, 25, 28, 29, 30, 31, 33, 35, 36, 38, 39, 41, 42, 43, 44, 47, 48, 52, 55, 56, 59, 60, 62]

elapsed time: 9570 milliseconds