#LIST OF PRIME NUMBERS IN ORDER CODE#

The code below uses a few Numpy tricks for a zippy implementation and generates 1 million primes in about. Ok Scruffy Pete has laid down the challenge in the comments section so I need to get serious about optimization. 4 seconds:ДЇor factor in range(3,1+int(math.sqrt(num)),2): The above is illustrative of efficiencies in using element-wise operations in Numpy arrays rather than looping.ДЄ good way of speeding up the above code even further is by breaking after finding the first modulo equal zero condition. Return filter(lambda num: (num % numpy.arange(2,1+int(math.sqrt(num)))).all(), range(2,upto+1))Д«y not including even numbers, we can run in half the time again to about. If we remove the for loop we cut the time to about 1.3 secs: Return filter(lambda num: numpy.array().all(), range(2,upto+1)) The following function uses a for loop to generate primes less than 100k and takes about 7 secs on my laptop: import numpy

The ones before that tell the story of how I got there. To cut the the chase, prime6 below is the fastest implementation.

Therefore, we can say that number 8 is a composite number.IвЂ™ve been looking at generating primes, and using various element-wise operations in Numpy arrays to do so. So the factors of 8 are 1, 2, 4, as well as 8. The number 8 can be written as 8 Г— 1, 1 Г— 8, 2 Г— 4, and 4 Г— 2. Therefore, we can say that number 6 is a composite number. So, the factors of number 6 are 1, 2, 3, and 6. Now, let us take a number, say 6, that can be written as 6 Г— 1, 1 Г— 6, 2 Г— 3, and 3 Г— 2. Therefore, we can say that 4 is a composite number as it has only 2 factors. It can be written as 4 Г— 1, 1 Г— 4, and 2 Г— 2 So the factors of 4 are 1, 2, and 4.

Total number of prime numbers from 1 to 1000 = 168Д¬omposite numbers are numbers that have at least one factor other than the number itself and 1. In other words, we can say that two is the only even prime number. Some of the properties of prime numbers are:Д®very number that is greater than 1 can be divided by at least one prime number.Д®very even positive integer greater than the number 2 can be expressed as the sum of two primes.Д®xcept for number 2, all other prime numbers are odd. Students can practice this method, by writing the positive integers from the numbers 1 to 1000 and circling the prime numbers, and putting a cross mark to all the composite numbers. Eratosthenes took the example of a sieve to filter out the prime numbers from a list of natural numbers and drain out the composite numbers. The prime number was discovered by Eratosthenes (275-194 B.C.). So any prime number should have only two factors and the number should be greater than 1. This means that number 1 can never be a prime number. Similarly, we can say for the numbers 2, 3, 5, 7, 13, 17, вЂ¦ etc can only be written in two forms with a single factor as 1, hence are the prime numbers.Д®ach prime number is only divisible by the number 1 and itself. So, we can say that 11 is a prime number. There is no other way of writing the number 11. Let us see a few examples of prime numbers and the list of prime numbers from 1 to 1000.ДЇor example, let us take a number for example 11. The prime number is known to be the simplest of a number. The numbers that have factors 1 and number itself are known as prime numbers.

Every prime number has exactly 2 factors.

List of prime numbers in order