How to resolve the algorithm Cullen and Woodall numbers step by step in the Wren programming language

Published on 12 May 2024 09:40 PM
#Wren

How to resolve the algorithm Cullen and Woodall numbers step by step in the Wren programming language

Table of Contents

Problem Statement

A Cullen number is a number of the form n × 2n + 1 where n is a natural number. A Woodall number is very similar. It is a number of the form n × 2n - 1 where n is a natural number. So for each n the associated Cullen number and Woodall number differ by 2. Woodall numbers are sometimes referred to as Riesel numbers or Cullen numbers of the second kind.

Cullen primes are Cullen numbers that are prime. Similarly, Woodall primes are Woodall numbers that are prime. It is common to list the Cullen and Woodall primes by the value of n rather than the full evaluated expression. They tend to get very large very quickly. For example, the third Cullen prime, n == 4713, has 1423 digits when evaluated.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Cullen and Woodall numbers step by step in the Wren programming language

Source code in the wren programming language

import "./big" for BigInt

var cullen = Fn.new { |n| (BigInt.one << n) * n + 1 }

var woodall = Fn.new { |n| cullen.call(n) - 2 }

System.print("First 20 Cullen numbers (n * 2^n + 1):")
for (n in 1..20) System.write("%(cullen.call(n)) ")

System.print("\n\nFirst 20 Woodall numbers (n * 2^n - 1):")
for (n in 1..20) System.write("%(woodall.call(n)) ")

System.print("\n\nFirst 2 Cullen primes (in terms of n):")
var count = 0
var n = 1
while (count < 2) {
    var cn = cullen.call(n)
    if (cn.isProbablePrime(5)){
        System.write("%(n) ")
        count = count + 1
    }
    n = n + 1
}

System.print("\n\nFirst 12 Woodall primes (in terms of n):")
count = 0
n = 1
while (count < 12) {
    var wn = woodall.call(n)
    if (wn.isProbablePrime(5)){
        System.write("%(n) ")
        count = count + 1
    }
    n = n + 1
}
System.print()


/* Cullen_and_woodall_numbers_2.wren */

import "./gmp" for Mpz

var cullen = Fn.new { |n| (Mpz.one << n) * n + 1 }

var woodall = Fn.new { |n| cullen.call(n) - 2 }

System.print("First 20 Cullen numbers (n * 2^n + 1):")
for (n in 1..20) System.write("%(cullen.call(n)) ")

System.print("\n\nFirst 20 Woodall numbers (n * 2^n - 1):")
for (n in 1..20) System.write("%(woodall.call(n)) ")

System.print("\n\nFirst 5 Cullen primes (in terms of n):")
var count = 0
var n = 1
while (count < 5) {
    var cn = cullen.call(n)
    if (cn.probPrime(15) > 0){
        System.write("%(n) ")
        count = count + 1
    }
    n = n + 1
}

System.print("\n\nFirst 12 Woodall primes (in terms of n):")
count = 0
n = 1
while (count < 12) {
    var wn = woodall.call(n)
    if (wn.probPrime(15) > 0){
        System.write("%(n) ")
        count = count + 1
    }
    n = n + 1
}
System.print()

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