function is_prime1 ( n )

c*********************************************************************72
c
cc is_prime1() determines whether an integer is prime.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    30 December 2022
c
c  Author:
c
c    John Burkardt
c
c  Input:
c
c    integer n: the value to be tested.
c
c  Output:
c
c    logical is_prime1: is true if the value is prime.
c
      implicit none

      integer i
      logical is_prime1
      integer n

      if ( n <= 1 ) then
        is_prime1 = .false.
        return
      end if

      is_prime1 = .true.

      do i = 2, n - 1
        if ( mod ( n, i ) == 0 ) then
          is_prime1 = .false.
          return
        end if
      end do

      return
      end
      function is_prime2 ( n )

c*********************************************************************72
c
cc is_prime2() determines whether an integer is prime.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    30 December 2022
c
c  Author:
c
c    John Burkardt
c
c  Input:
c
c    integer n: the value to be tested.
c
c  Output:
c
c    logical is_prime2: is true if the value is prime.
c
      implicit none

      integer i
      logical is_prime2
      integer n
      integer n_sqrt

      if ( n <= 1 ) then
        is_prime2 = .false.
        return
      end if

      if ( n == 2 .or. n == 3 ) then
        is_prime2 = .true.
        return
      end if

      is_prime2 = .true.

      n_sqrt = int ( sqrt ( real ( n ) ) )

      do i = 2, n_sqrt
        if ( mod ( n, i ) == 0 ) then
          is_prime2 = .false.
          return
        end if
      end do

      return
      end
      function is_prime3 ( n )

c*********************************************************************72
c
cc is_prime3() determines whether an integer is prime.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    30 December 2022
c
c  Author:
c
c    John Burkardt
c
c  Input:
c
c    integer n: the value to be tested.
c
c  Output:
c
c    logical is_prime3: is true if the value is prime.
c
      implicit none

      integer i
      integer ihi
      logical is_prime3
      integer n

      if ( n <= 1 ) then
        is_prime3 = .false.
        return
      end if

      if ( ( n == 2 ) .or. ( n == 3 ) ) then
        is_prime3 = .true.
        return
      end if

      if ( ( mod ( n, 2 ) == 0 ) .or. ( mod ( n, 3 ) == 0 ) ) then
        is_prime3 = .false.
        return
      end if

      ihi = int ( sqrt ( real ( n ) ) )

      do i = 5, ihi, 6
        if ( ( mod ( n, i ) == 0 ) .or. ( mod ( n, i + 2 ) == 0 ) ) then
          is_prime3 = .false.
          return
        end if
      end do

      is_prime3 = .true.

      return
      end