R Examples

R Program to Check Prime Number

A Prime number is a natural number greater than 1 and divisible by 1 and itself only, for example: 2, 3, 5, 7, etc.

Method 1: Using conditional statements

In the example below, the number called MyNum is checked for prime number by dividing it with all natural numbers starting from 2 to N - 1.

MyNum <- 17
n <- 0
Numbers <- c(2:(MyNum-1))

for (i in Numbers){
  if (MyNum %% i == 0) {
    n <- n + 1
    break    
  }
}

if (MyNum <= 1) {
  sprintf("%d is not a prime number.", MyNum)
} else if (MyNum == 2) {
  sprintf("%d is a prime number.", MyNum)
} else if (n == 0) {
  sprintf("%d is a prime number.", MyNum)
} else {
  sprintf("%d is not a prime number.", MyNum)
}

The above code will give the following output:

[1] "17 is a prime number."

Method 2: Using function

In the example below, a function called primenumber() is created which takes a number as argument and checks it for prime number by dividing it with all natural numbers starting from 2 to N/2.

primenumber <- function(MyNum) {
  n <- 0
  i <- 2
  Numbers <- c(2:(MyNum%/%2 + 1))
  
  for (i in Numbers) {
    if (MyNum %% i == 0) {
      n <- n + 1
      break      
    }
  }

  if (MyNum <= 1) {
    sprintf("%d is not a prime number.", MyNum)
  } else if (MyNum == 2) {
    sprintf("%d is a prime number.", MyNum)
  } else if (n == 0) {
    sprintf("%d is a prime number.", MyNum)
  } else {
    sprintf("%d is not a prime number.", MyNum)
  }
}

primenumber(21)

The above code will give the following output:

[1] "21 is not a prime number."

Method 3: Optimized Code

Instead of checking the divisibility of given number from 2 to N/2, it is checked till square root of N. For a factor larger than square root of N, there must the a smaller factor which is already checked in the range of 2 to square root of N.
Except from 2 and 3, every prime number can be represented into 6k ± 1.

primenumber <- function(MyNum) {
  n <- 0
  i <- 2
  if (MyNum == 2 || MyNum == 3) {
    sprintf("%d is a prime number.", MyNum)
  } else if (MyNum %% 6 == 1 || MyNum %% 6 == 5) {
    while (i*i <= MyNum) {
      if (MyNum %% i == 0) {
        n <- n + 1
        break        
      }
      i <- i + 1       
    }

    if (n == 0) {
      sprintf("%d is a prime number.", MyNum)
    } else {
      sprintf("%d is not a prime number.", MyNum)    
    }
  } else {
    sprintf("%d is not a prime number.", MyNum)
  }
}

primenumber(21)

The above code will give the following output:

[1] "21 is not a prime number."