How to resolve the algorithm Sequence of primes by trial division step by step in the Julia programming language
How to resolve the algorithm Sequence of primes by trial division step by step in the Julia programming language
Table of Contents
Problem Statement
Generate a sequence of primes by means of trial division.
Trial division is an algorithm where a candidate number is tested for being a prime by trying to divide it by other numbers. You may use primes, or any numbers of your choosing, as long as the result is indeed a sequence of primes. The sequence may be bounded (i.e. up to some limit), unbounded, starting from the start (i.e. 2) or above some given value. Organize your function as you wish, in particular, it might resemble a filtering operation, or a sieving operation. If you want to use a ready-made is_prime function, use one from the Primality by trial division page (i.e., add yours there if it isn't there already).
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Sequence of primes by trial division step by step in the Julia programming language
The provided Julia code defines a custom Julia struct TDPrimes
designed to generate prime numbers up to a specified limit. Here's how this code works:
-
TDPrimes
Struct:- The
TDPrimes
struct is defined as a parametric type with one parameter,T
, which must be a subtype ofInteger
. - It has a single field named
uplim
that specifies the upper limit up to which prime numbers should be generated.
- The
-
Starting the Prime Number Generator:
- The
start
function for theTDPrimes
struct initializes the generation of prime numbers by returning the first prime number, 2, as a one-element vector of typeT
.
- The
-
Checking if Generation is Done:
- The
done
function checks if the generation of prime numbers is complete. It returnstrue
if the last element of the input vectorp
is greater than theuplim
field of thepl
struct, indicating that no more primes belowuplim
remain.
- The
-
Generating the Next Prime Number:
- The
next
function generates the next prime number and updates the input vectorp
accordingly. - It initializes
pr
to the last element ofp
(the current prime) and incrementsnpr
until it finds the next prime number. - The
npr
value is checked against all the elements inp
using the%
(modulo) operator to ensure that it is not divisible by any of the previously found prime numbers. This check verifies thatnpr
is a prime number. - Once a prime number
npr
is found, it is appended top
, and the current primepr
is returned as the second output of the function.
- The
-
Printing Prime Numbers:
- Outside the
TDPrimes
struct definition, the code generates prime numbers up to 100 by creating an instance ofTDPrimes(100)
and iterating over its values. - The prime numbers are collected in a vector and then joined together with commas to create a string representation.
- The resulting string is printed to the console, displaying the prime numbers less than or equal to 100.
- Outside the
In summary, this code provides an efficient way to generate prime numbers up to a specified limit using a custom Julia struct, TDPrimes
. The start
, done
, and next
functions work together to incrementally find and store prime numbers in a vector until the desired limit is reached.
Source code in the julia programming language
struct TDPrimes{T<:Integer}
uplim::T
end
Base.start{T<:Integer}(pl::TDPrimes{T}) = 2ones(T, 1)
Base.done{T<:Integer}(pl::TDPrimes{T}, p::Vector{T}) = p[end] > pl.uplim
function Base.next{T<:Integer}(pl::TDPrimes{T}, p::Vector{T})
pr = npr = p[end]
ispr = false
while !ispr
npr += 1
ispr = all(npr % d != 0 for d in p)
end
push!(p, npr)
return pr, p
end
println("Primes ≤ 100: ", join((p for p in TDPrimes(100)), ", "))
You may also check:How to resolve the algorithm Check Machin-like formulas step by step in the Julia programming language
You may also check:How to resolve the algorithm Real constants and functions step by step in the Elm programming language
You may also check:How to resolve the algorithm Pseudo-random numbers/PCG32 step by step in the uBasic/4tH programming language
You may also check:How to resolve the algorithm Narcissistic decimal number step by step in the Factor programming language
You may also check:How to resolve the algorithm Department numbers step by step in the Objeck programming language