Prime Number with Simple for loop not working? - algorithm

Im trying to solve a problem where I have to use a for loop in solving if a number is prime or not. It seems like it only picks up if the number is divided by two to determine if it is prime or not. My code doesn't pick up if it is divisible by 3 and up though...
Here is my code:
def isPrime(num):
for i in range (2,num):
if (num%i) !=0:
return True
else:
return False
isPrime(15)
I know 15 is not a prime number but it is returning True instead of False. Can anyone help? Thanks

OP's algorithm always exits on the first iteration.
Instead, loop less often and only exit loop when a divisor is found. Also account for values less than 2.
def isPrime(num):
for i in range [2,isqrt(num)]:
if (num%i == 0) return False
if (num < 2) return False
return True

Related

How to use for loop to find a prime number?

def check_prime(x):
for i in range(2,x):
if x%i==0:
return False
else: return True
Why is this code not working properly. This code returns true even for some non prime numbers. eg:- 9 , 25 ,...
You are returning True right away when you find one number that doesn't divide x, which is wrong. You're supposed to return True when all number greater or equal to 2 and less than x doesn't divide x. To fix this, remove the else code, and return True after the for loop is over.
Here's the full code:
def check_prime(x):
for i in range(2, x):
if x % i == 0:
return False
return True

Why is my ruby script execution too long?

I am trying to solve a problem from http://www.beatmycode.com/challenge/5/take, and I wrote a script:
def is_prime?(num)
(2...num).each do |divisor|
return false if num % divisor == 0
end
true
end
def circular_prime(num)
circular_primes = []
if num < 2
return false
end
(2..num-1).each do |number|
is_prime?(number)
result = [number.to_s]
(0..number.to_s.size-2).each do |x|
var = result.last.split('')
result << var.unshift(var.pop).join if var.uniq.size != 1
end
circular_primes << result if result.all?{ |x| is_prime? x.to_i }
end
end
When I tested it with 10,100,1000, and 10_000, the script executed very fast, but when I tested with 100_000, the shell displayed an Interrupt error. Where is the weak point, and how can I fix it?
Your is_prime? method is too slow. Some minor improvement could be:
You don't have to test divisor all the way upto num, the square root of
num is enough.
You can skip all even numbers since 2 is the only even prime
number.
However, this is still not good enough because the algorithm is slow. Since you need to generate prime numbers among consecutive integers, consider using Sieve of Eratosthenes.
Of course there's prime standard library but I assume you want to do this manually.
This script's time complexity is O(n^2), so it's expected that it will take long time to finish for big input. Try using https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes to find primes and remembering which number is a prime in some array.

How to create a method that returns the nth prime number?

I'm trying to write a method that returns the nth prime number.
I've worked out a solution but the problem is in my method. I create a large array of numbers that seems to process super slow. (1..104729).to_a to be exact. I chose 104729 because the max n can be is 10000 and the 10000th integer is 104729. I'm looking for a way to optimize my method.
Is 104729 is too large a value? Is there a way to write this so that I'm not creating a large array?
Here's the method:
def PrimeMover(num)
def is_prime(x)
i = 0
nums = (2..x).to_a
while nums[i] < nums.max
if x % nums[i] != 0
i += 1
else
return false
end
end
return true
end
primes_arr = (3..104729).to_a.select {|y| is_prime(y)}
primes_arr[num]
end
require "prime"
def find_prime(nth)
Prime.take(nth).last
end
Combine Ruby's built-in prime library, and a lazy enumerator for performance:
require 'prime'
(1...100_000).lazy.select(&:prime?).take(100).to_a
Or simply, as highlighted by Arturo:
Prime.take(100)
You can use Ruby's built in #prime? method, which seems pretty efficient.
The code:
require 'prime'
primes_arr = (3..104729).to_a.select &:prime?
runs in 2-3 seconds on my machine, which I find somewhat acceptable.
If you need even better performance or if you really need to write your own method, try implementing the Sieve of Erathostenes. Here are some Ruby samples of that: http://rosettacode.org/wiki/Sieve_of_Eratosthenes#Ruby
Here's an optimal a trial division implementation of is_prime without relying on the Prime class:
A prime number is a whole number divisible only by 1 and itself, and 1 is not prime. So we want to know if x divides into anything less than x and greater than 1. So we start the count at 2, and we end at x - 1.
def prime?(x)
return false if x < 2
2.upto(x - 1) do |n|
return false if (x % n).zero?
end
true
end
As soon as x % n has a remainder, we can break the loop and say this number is not prime. This saves you from looping over the entire range. If all the possible numbers were exhausted, we know the number is prime.
This is still not optimal. For that you would need a sieve, or a different detection algorithm to trial division. But it's a big improvement on your code. Taking the nth up to you.

Comparing two Integers by their divisibility

For instance:
8 > 10 = true, since 8 is divisible by 2 three times and 10 only once.
How can I compare two integers from any range of numbers? Are the modulo and divide operator capable of doing this task?
Use binary caculate to judge it
def devided_by_two(i)
return i.to_s(2).match(/0*$/).to_s.count('0')
end
To make integer divisibility by 2, just transcode it to binary and judge how many zero from end of banary number. The code I provide can be more simple I think.
Yes, they are capable. A number is even if, when you divide it by two, the remainder is zero.
Hence, you can use a loop to continuously divide by two until you get an odd number, keeping a count of how many times you did it.
The (pseudo-code) function for assigning a "divisibility by two, continuously" value to a number would be something like:
def howManyDivByTwo(x):
count = 0
while x % 2 == 0:
count = count + 1
x = x / 2 # make sure integer division
return count
That shouldn't be too hard to turn into Ruby (or any procedural-type language, really), such as:
def howManyDivByTwo(x)
count = 0
while x % 2 == 0
count = count + 1
x = x / 2
end
return count
end
print howManyDivByTwo(4), "\n"
print howManyDivByTwo(10), "\n"
print howManyDivByTwo(11), "\n"
print howManyDivByTwo(65536), "\n"
This outputs the correct:
2
1
0
16
Astute readers will have noticed there's an edge case in that function, you probably don't want to try passing zero to it. If it was production code, you'd need to catch that and act intelligently since you can divide zero by two until the cows come home, without ever reaching an odd number.
What value you return for zero depends on needs you haven't specified in detail. Theoretically (mathematically), you should return infinity but I'll leave that up to you.
Notice that you will likely mess up much of your code if you redefine such basic method. Knowing that, this is how it's done:
class Integer
def <=> other
me = self
return 0 if me.zero? and other.zero?
return -1 if other.zero?
return 1 if me.zero?
while me.even? and other.even?
me /= 2
other /= 2
end
return 0 if me.odd? and other.odd?
return -1 if me.odd?
return 1 if other.odd? # This condition is redundant, but is here for symmetry.
end
end

How can I test if a value is a prime number in Ruby? Both the easy and the hard way?

I am trying to create a program that will test whether a value is prime, but I don't know how. This is my code:
class DetermineIfPrime
def initialize (nth_value)
#nth_value = nth_value
primetest
end
def primetest
if Prime.prime?(#nth_value)
puts ("#{#nth_value} is prime")
else
puts ("This is not a prime number.")
end
rescue Exception
puts ("#{$!.class}")
puts ("#{$!}")
end
end
And every time I run that it returns this.
NameError
uninitialized constant DetermineIfPrime::Prime
I tried other ways to do the job, but I think this is the closest I can get.
I also tried this:
class DetermineIfPrime
def initialize (nth_value)
#nth_value = nth_value
primetest
end
def primetest
for test_value in [2, 3, 5, 7, 9, 11, 13] do
if (#nth_value % test_value) == 0
puts ("#{#nth_value} is not divisible by #{test_value}")
else
puts ("This is not a prime number since this is divisible by #{test_value}")
break
end
end
end
end
Or am I just doing something wrong?
Ruby has built in method to check if number is prime or not.
require 'prime'
Prime.prime?(2) #=> true
Prime.prime?(4) #=> false
def is_prime?(num)
return false if num <= 1
Math.sqrt(num).to_i.downto(2).each {|i| return false if num % i == 0}
true
end
First, we check for 0 and 1, as they're not prime. Then we basically just check every number less than num to see if it divides. However, as explained here, for every factor greater than the square root of num, there's one that's less, so we only look between 2 and the square root.
Update
def is_prime?(num)
return if num <= 1
(2..Math.sqrt(num)).none? { |i| (num % i).zero? }
end
The error you are getting is because you haven't required Primein your code, You need to do require Prime in your file.
One cool way I found here, to check whether a number is prime or not is following:
class Fixnum
def prime?
('1' * self) !~ /^1?$|^(11+?)\1+$/
end
end
10.prime?
From an algorithmic standpoint, checking if a number is prime can be done by checking all numbers up to and including (rounding down to previous integer) said number's square root.
For example, checking if 100 is prime involves checking everything up to 10.
Checking 99 means only going to 9.
** Another way to think about it **
Each factor has a pair (3 is a factor of 36, and 3's pair is 12).
The pair is on the other side of the square root (square root of 6 is 36, 3 < 6, 12 > 6).
So by checking everything until the square root (and not going over) ensures you check all possible factors.
You can make it quicker by having a list of prime numbers to compare, as you are doing. If you have a maximum limit that's reasonably small, you could just have a list of primes and do a direct lookup to see if that number is prime.
def is_prime?(num)
Math.sqrt(num).floor.downto(2).each {|i| return false if num % i == 0}
true
end
lol sorry for resurrecting a super old questions, but it's the first one that came up in google.
Basically, it loops through possible divisors, using the square root as the max number to check to save time on very large numbers.
In response to your question, while you can approach the problem by using Ruby's Prime I am going to write code to answer it on its own.
Consider that all you need to do is determine a factor that is smaller than the integer's square root. Any number larger than the integer's square root as a factor requires a second factor to render the number as the product. (e.g. square root of 15 is approx 3.8 so if you find 5 as a factor it is only a factor with the factor pair 3 and 5!!)
def isPrime?(num)
(2..Math.sqrt(num)).each { |i| return false if num % i == 0}
true
end
Hope that helps!!
(To first answer the question: yes, you are doing something wrong. As BLUEPIXY mentions, you need to put require 'prime' somewhere above the line that calls Prime.prime?. Typically on line 1.)
Now, a lot of answers have been given that don't use Prime.prime?, and I thought it might be interesting to benchmark some of them, along with a possible improvement of my own that I had in mind.
###TL;DR
I benchmarked several solutions, including a couple of my own; using a while loop and skipping even numbers performs best.
Methods tested
Here are the methods I used from the answers:
require 'prime'
def prime1?(num)
return if num <= 1
(2..Math.sqrt(num)).none? { |i| (num % i).zero? }
end
def prime2?(num)
return false if num <= 1
Math.sqrt(num).to_i.downto(2) {|i| return false if num % i == 0}
true
end
def prime3?(num)
Prime.prime?(num)
end
def prime4?(num)
('1' * num) !~ /^1?$|^(11+?)\1+$/
end
prime1? is AndreiMotinga's updated version. prime2? is his original version (with the superfluous each method removed). prime3? is Reboot's, using prime library. prime4? is Saurabh's regex version (minus the Fixnum monkey-patch).
A couple more methods to test
The improvement I had in mind was to leverage the fact that even numbers can't be prime, and leave them out of the iteration loop. So, this method uses the #step method to iterate over only odd numbers, starting with 3:
def prime5?(num)
return true if num == 2
return false if num <= 1 || num.even?
3.step(Math.sqrt(num).floor, 2) { |i| return false if (num % i).zero? }
true
end
I thought as well that it might be interesting to see how a "primitive" implementation of the same algorithm, using a while loop, might perform. So, here's one:
def prime6?(num)
return true if num == 2
return false if num <= 1 || num.even?
i = 3
top = Math.sqrt(num).floor
loop do
return false if (num % i).zero?
i += 2
break if i > top
end
true
end
Benchmarks
I did a simple benchmark on each of these, timing a call to each method with the prime number 67,280,421,310,721. For example:
start = Time.now
prime1? 67280421310721
puts "prime1? #{Time.now - start}"
start = Time.now
prime2? 67280421310721
puts "prime2? #{Time.now - start}"
# etc.
As I suspected I would have to do, I canceled prime4? after about 60 seconds. Presumably, it takes quite a bit longer than 60 seconds to assign north of 6.7 trillion '1''s to memory, and then apply a regex filter to the result — assuming it's possible on a given machine to allocate the necessary memory in the first place. (On mine, it would seem that there isn't: I went into irb, put in '1' * 67280421310721, made and ate dinner, came back to the computer, and found Killed: 9 as the response. That looks like a SignalException raised when the process got killed.)
The other results are:
prime1? 3.085434
prime2? 1.149405
prime3? 1.236517
prime5? 0.748564
prime6? 0.377235
Some (tentative) conclusions
I suppose that isn't really surprising that the primitive solution with the while loop is fastest, since it's probably closer than the others to what's going on under the hood. It is a bit surprising that it's three times faster than Prime.prime?, though. (After looking at the source code in the doc it is less so. There are lots of bells and whistles in the Prime object.)
AndreiMotinga's updated version is nearly three times as slow as his original, which suggests that the #none? method isn't much of a performer, at least in this context.
Finally, the regex version might be cool, but it certainly doesn't appear to have much practical value, and using it in a monkey-patch of a core class looks like something to avoid entirely.
If you are going to use any Prime functions you must include the Prime library. This problem can be solved without the use of the prime library however.
def isPrime?(num)
(2..Math.sqrt(num)).each { |i|
if num % i == 0 && i < num
return false
end
}
true
end
Something like this would work.
Try this
def prime?(num)
2.upto(Math.sqrt(num).ceil) do |i|
break if num%i==0
return true if i==Math.sqrt(num).ceil
end
return false
end
So most of the answers here are doing the same thing in slightly different ways which is one of the cool things about Ruby, but I'm a pretty new student (which is why I was looking this up in the first place) and so here's my version with comment explanations in the code:
def isprime n # starting with 2 because testing for a prime means you don't want to test division by 1
2.upto(Math.sqrt(n)) do |x| # testing up to the square root of the number because going past there is excessive
if n % x == 0
# n is the number being called from the program
# x is the number we're dividing by, counting from 2 up to the square root of the number
return false # this means the number is not prime
else
return true # this means the number is prime
end
end
end

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