Gen_Prime

A way to transform a hash to a prime number.

Explaining

This is a method that allows calculate a prime number using a hash. The idea is really simple: we generate a number n passing the hash from 16-basis to a special basis, taken the value of tha char in 10-basis and multiply by 2^i, where i is the position of the char in the string. This number n, we calculate the rest module 31, obtaining an other number d. We find the numbers x=2^d-1 and y=2^(d+1)-1. We call a function that returns the first prime nuber in [x,y]. This will be our choice.

We apply module 31 for 2 reasons:

1. Every prime generate will be lower than 2³².
2. We can work with up 2⁵¹². If every prime is lower than 2³², we can use 16 or more hashes.

[dependencies]
Gen_Prime = "1.1.5"
 

Examples

EXAMPLE 1

extern crate primes;
 
 
# fn main() {
     let z:u128;
     println!("Introduce a hash");
     let mut a = String::new();
     std::io::stdin().read_line(&mut a).expect("Fail");
     let v : Vec<&str>=a.split("").collect();
     z=primes::hash_to_prime(v);
     println!("{}", z);

# } 
 

Outputs:

Introduce a hash

a123dfe4758bc27237a

2147483647

Introduce a hash

074a4a47c445cf604b2ca687fed09fd8f3a78a16d20786b1a97aa6642fe0f87a8577a52cbace36bab6a6c40c3f1843be

1073741827

Introduce a hash

00eccf559792ee42e3ea26e394e9ab52ce569e47504d44715102cc0c2ab4f542dc54c383e8e13d360ebc57c5ede5e64b

16777259

Introduce a hash

daa41c63b728ba70e6c377d7d17d9e53185fc720e7e6326626608eb1edc3735f67d963c303d92c9196583f3cd8739943

16553

EXAMPLE 2

use std::io;
use std::u128;
extern crate bigint;
extern crate primes;
extern crate rand;
use bigint::U512;
 
# fn main() { 
     let mut mult:bigint::U512;
     mult=U512::one();
     loop{
         println!("Introduce a hash");
         let mut a = String::new();
         std::io::stdin().read_line(&mut a).expect("Fail");
         let v : Vec<&str>=a.split("").collect();
         let n2=v.len() as u32;
         let res:u128;
         let mut v2=Vec::with_capacity((n2-3) as usize);
         for i in 0..n2-3 {
             i as usize;
             v2.push(v[(i+1) as usize]);
         } //this lines are to safe each char in one component of a vector, and to delete white spaces
         res=primes::hash_to_prime(v2); //Generating a prime
         mult=mult*(bigint::U512::from(res as usize)); //Product of the primes
         println!("Do you want to enter another hash?[Y/N]");
         let mut b = String::new();
         io::stdin().read_line(&mut b).expect("Fail");
         let b : char = b.trim().parse().expect("Please, input one choice");
         if b=='N' || b=='n'{
             break;
         }
     }
     println!("{}", mult);
# }
 

Output

Introduce a hash

daa41c63b728ba70e6c377d7d17d9e53185fc720e7e6326626608eb1edc3735f67d963c303d92c9196583f3cd8739943

19

r:100

Do you want to enter another hash?[Y/N]

Y

Introduce a hash

0907b5ff1b7d6f7b2639ca00565c8f42cbf7529b992f825b2676ec30c294b477b913476d6a508da9d195f1dacc893173

23

r:39

Do you want to enter another hash?[Y/N]

Y

Introduce a hash

4cb34fd780fbac405a433f428bd5672c0f7003cf1ae9d0675225c8d83783c0fc57e8b1f64a9bad799084f71381d1115e

27

r:55

Do you want to enter another hash?[Y/N]

Y

Introduce a hash

fae89ae85b629f1d5263c7b5ad5035cc72c3cb02f95a9a242f5065f235611863f28fd4798818054e4cf69fd464e7f3b0

8

r:49

Do you want to enter another hash?[Y/N]

Y

Introduce a hash

d0054fddab35b4aa7ab1356811f5c5ef7a1536ccca1ac76549b36030c875c4329d12f86b67591e3d9b3ca7f178861c94

5

r:57

Do you want to enter another hash?[Y/N]

N

110277345636720260972118701 where the number after each hash is the value mod 31 (d) and r is a rand number that calculates the rth prime in [x,y]. The last number is the product of all primes. Can you find one of the primes? ;)