is_prime3 <- function ( n ) 

#*****************************************************************************80
#
## is_prime3() reports whether an integer is prime.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    29 December 2022
#
#  Author:
#
#    John Burkardt.
#
#  Input:
#
#    integer n: the value to be tested.
#
#  Output:
#
#    logical value: true if n is a prime.
#
{
  if ( n <= 1 )
  {
    return ( FALSE )
  }

  if ( n <= 3 )
  {
    return ( TRUE )
  }

  if ( ( n %% 2 == 0 ) || ( n %% 3 == 0 ) )
  {
    return ( FALSE )
  }

  i <- 5
  while ( i * i <= n )
  {
    if ( ( n %% i == 0 ) || ( n %% ( i + 2 ) == 0 ) )
    {
      return ( FALSE )
    }
    i = i + 6
  }

  return ( TRUE )
}