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## Python Examples

Check if a Number is Positive, Negative or 0

- Check if a Number is Odd or Even
- Check Leap Year
- Find the Largest Among Three Numbers
- Check Prime Number

Print all Prime Numbers in an Interval

Find the Factorial of a Number

## Related Topics

- Python while Loop
- Python range()
- Python break and continue
- Python for Loop
- Python if...else Statement
- Python Looping Techniques

## Python Program to Check Prime Number

## Example 1: Using a flag variable

Outside the loop, we check if flag is True or False .

Note : We can improve our program by decreasing the range of numbers where we look for factors.

In the above program, our search range is from 2 to num - 1 .

## Example 2: Using a for...else statement

Here, we have used a for..else statement to check if num is prime.

So, in the else clause, we print that the number is prime.

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- Mathematical Algorithms
- Check if a large number is divisible by 3 or not
- Check if a large number is divisible by 4 or not
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- Check divisibility by 7
- Check if a large number is divisible by 9 or not
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## Prime Numbers

- Left-Truncatable Prime
- Mersenne Prime
- Super Prime
- Hardy-Ramanujan Theorem
- Rosser’s Theorem
- Fermat’s little theorem
- Introduction to Primality Test and School Method
- Vantieghems Theorem for Primality Test
- AKS Primality Test
- Lucas Primality Test
- Efficient program to print all prime factors of a given number
- Smith Number
- Sphenic Number
- Hoax Number
- k-th prime factor of a given number
- Pollard’s Rho Algorithm for Prime Factorization
- Finding power of prime number p in n!
- Find all factors of a Natural Number
- Find numbers with n-divisors in a given range
- Modular Exponentiation (Power in Modular Arithmetic)
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- Euler’s criterion (Check if square root under modulo p exists)
- Find sum of modulo K of first N natural number
- How to compute mod of a big number?
- Exponential Squaring (Fast Modulo Multiplication)
- Trick for modular division ( (x1 * x2 …. xn) / b ) mod (m)
- Program for factorial of a number
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- Count trailing zeroes in factorial of a number
- Find the Factorial of a large number
- Primorial of a number
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- Check if a number is a Krishnamurthy Number or not
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- Program for Fibonacci numbers
- Interesting facts about Fibonacci numbers
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- Find nth Fibonacci number using Golden ratio
- Matrix Exponentiation
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- Program to calculate value of nCr
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- Sum of squares of binomial coefficients
- Space and time efficient Binomial Coefficient
- Horner’s Method for Polynomial Evaluation
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- Bell Numbers (Number of ways to Partition a Set)
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- Prime Factorization using Sieve O(log n) for multiple queries
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- Introduction to Chinese Remainder Theorem
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- Cyclic Redundancy Check and Modulo-2 Division
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- Interquartile Range (IQR)
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- Implement *, – and / operations using only + arithmetic operator
- Difficulty Level : Easy
- Discuss(20+)

## What are prime numbers?

- In other words, the prime number is a positive integer greater than 1 that has exactly two factors, 1 and the number itself.
- There are many prime numbers, such as 2, 3, 5, 7, 11, 13, etc.
- Keep in mind that 1 cannot be either prime or composite.
- The remaining numbers, except for 1, are classified as prime and composite numbers.

## Some interesting facts about Prime numbers:

- Except for 2, which is the smallest prime number and the only even prime number, all prime numbers are odd numbers.
- Every prime number can be represented in form of 6n + 1 or 6n – 1 except the prime numbers 2 and 3, where n is a natural number.
- Two and Three are only two consecutive natural numbers that are prime.
- Goldbach Conjecture: Every even integer greater than 2 can be expressed as the sum of two primes.
- Wilson Theorem : Wilson’s theorem states that a natural number p > 1 is a prime number if and only if
- Fermat’s Little Theorem : If n is a prime number, then for every a, 1 <= a < n,
- Prime Number Theorem : The probability that a given, randomly chosen number n is prime is inversely proportional to its number of digits, or to the logarithm of n.
- Lemoine’s Conjecture : Any odd integer greater than 5 can be expressed as a sum of an odd prime (all primes other than 2 are odd) and an even semiprime. A semiprime number is a product of two prime numbers. This is called Lemoine’s conjecture.

## Properties of prime numbers:

- Every number greater than 1 can be divided by at least one prime number.
- Every even positive integer greater than 2 can be expressed as the sum of two primes.
- Except 2, all other prime numbers are odd. In other words, we can say that 2 is the only even prime number.
- Two prime numbers are always coprime to each other.
- Each composite number can be factored into prime factors and individually all of these are unique in nature.

## Prime numbers and co-prime numbers:

- A coprime number is always considered as a pair, whereas a prime number is considered as a single number.
- Co-prime numbers are numbers that have no common factor except 1. In contrast, prime numbers do not have such a condition.
- A co-prime number can be either prime or composite, but its greatest common factor (GCF) must always be 1. Unlike composite numbers, prime numbers have only two factors, 1 and the number itself.
- Example of co-prime: 13 and 15 are co-primes. The factors of 13 are 1 and 13 and the factors of 15 are 1, 3 and 5. We can see that they have only 1 as their common factor, therefore, they are coprime numbers.
- Example of prime: A few examples of prime numbers are 2, 3, 5, 7 and 11 etc.

## How do we check whether a number is Prime or not?

Time Complexity: O(sqrt(n)) Auxiliary space: O(1)

Efficient approach: To check whether the number is prime or not follow the below idea:

In the previous approach given if the size of the given number is too large then its square root will be also very large, so to deal with large size input we will deal with a few numbers such as 1, 2, 3, and the numbers which are divisible by 2 and 3 in separate cases and for remaining numbers, we will iterate our loop from 5 to sqrt(n) and check for each iteration whether that (iteration) or (that iteration + 2) divides n or not. If we find any number that divides, we return false.

Below is the implementation for the above idea:

Time complexity: O(sqrt(n)) Auxiliary space: O(1)

Approach 3: To check the number is prime or not using recursion follow the below idea:

Recursion can also be used to check if a number between 2 to n – 1 divides n. If we find any number that divides, we return false.

Below is the implementation for the below idea:

Time Complexity: O(N) Auxiliary Space: O(N)

Approach 4: To check the number is prime or not using Fermat’s little theorem with out using loop

Time complexity: O(1) Auxiliary space: O(1)

- Primality Test | Set 1 (Introduction and School Method)
- Primality Test | Set 2 (Fermat Method)
- Primality Test | Set 3 (Miller–Rabin)
- Primality Test | Set 4 (Solovay-Strassen)

Algorithms to find all prime numbers smaller than the N.

More problems related to Prime number

- Find two distinct prime numbers with a given product
- Print all prime numbers less than or equal to N
- Recursive program for prime number
- Find two prime numbers with a given sum
- Find the highest occurring digit in prime numbers in a range
- Program to print all prime factors of a given number
- Least prime factor of numbers till n
- Prime factors of LCM of array elements – GeeksforGeeks
- Program for Goldbach’s Conjecture
- Prime numbers and Fibonacci
- Composite Number
- Recent Articles on Prime Numbers!

Solve DSA problems on GfG Practice.

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## C Program to Check whether the Given Number is a Prime

C programming examples tutorial index.

A prime number is a natural number that has only one and itself as factors.

Above numbers can only be divided evenly by 1 or itself , so these numbers are prime numbers.

## Prime Number Check Program in C

## C program example for prime number:

A number is considered as prime number when it satisfies the below conditions.

- It should be whole number
- It should be greated than 1
- It should have only 2 factors. They are, 1 and the number itself.

Example for prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23 etc.

Why 4, 6, 8, 9, 10, 12, 14, 15, 16 etc are not prime numbers?

## Example C program for prime number:

Output of c program for prime number:, other c programs:.

- C program for factorial
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## Prime Number Program In C

Few prime number are − 1, 2, 3, 5 , 7, 11 etc.

Algorithm of this program is very easy −

## Flow Diagram

We can draw a flow diagram for this program as given below −

We can draft a pseudocode of the above algorithm as follows −

## Implementation

Implementation of this algorithm is given below −

Output of the program should be −

## Introduction to Python

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Python career opportunities: your career guide to python programming.

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## What is a Prime Number?

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## Python Program to Check Prime Number

There are different ways to optimize the prime number program in Python:

- Instead of checking till n, we can check till √n because a larger factor of n must be a multiple of smaller factor that has been already checked.
- The algorithm can be improved further by observing that all primes are of the form 6k ± 1, with the exception of 2 and 3. This is because all integers can be expressed as (6k + i) for some integer k and for i = ?1, 0, 1, 2, 3, or 4; 2 divides (6k + 0), (6k + 2), (6k + 4); and 3 divides (6k + 3). So a more efficient method is to test if n is divisible by 2 or 3, then to check through all the numbers of form 6k ± 1.

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## Python Program for Prime Number

## Python Program to Check Prime Number

- The first thing you need to check in the program is that the input variable must be greater than 1 as mentioned above prime number is greater than 1.
- The second thing you need to check is if the input num is exactly divisible by any number from 2 to num - 1. If in case you find a factor in that range, then the number is not prime or else the number is prime.

## 1) Check Prime Number Using For Loop

## 2) Check Prime Number Using While Loop

If the flag value is 1, the string "9 is not a prime number" is displayed.

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## IMAGES

## VIDEO

## COMMENTS

Program to Check Prime Number ... Enter a positive integer: 29 29 is a prime number. In the program, a for loop is iterated from i = 2 to i < n/2 . ... If n is

We could have used the range, range(2,num//2) or range(2,math.floor(math.sqrt(num)+1)) . The latter range is based on the fact that a composite number must have

Prime Numbers ; C++. // C++ program to check whether a number. // is prime or not using recursion. #include <iostream>. using namespace std; ; Java. // Java

#include<stdio.h> · int main(){ · int n,i,m=0,flag=0; · printf("Enter the number to check prime:"); · scanf("%d",&n); · m=n/2; · for(i=2;i<=m;i++) · {

Prime Number Check Program in C · 1st iteration: i = 1; i <= 5; i++ here i is incremented i.e. i value for next iteration is 2 · 2nd iteration: i = 2; i <= 5; i++

Algorithm to Find Prime Number. STEP 1: Take num as input. STEP 2: Initialize a variable temp to 0. STEP 3: Iterate a “for”

Example C program for prime number: · main() · int i, num, p = 0; · printf("Please enter a number: \n"); · scanf("%d", &num); · for(i=1; i<=num; i++) · { · if(num%i==0).

Few prime number are − 1, 2, 3, 5 , 7, 11 etc. Algorithm. Algorithm of this program is very easy − START Step 1 → Take integer variable A Step 2 → Divide

The numbers 2, 3, 5, 7, etc. are prime numbers as they do not have any other factors. To find a prime number in Python, you have to iterate the value from start

2) Check Prime Number Using While Loop ... In the program, the input method is used for fetching a number from the user to evaluate if it is a prime number. After