Q:

Mersenne Prime Oracle

Please give me any feedback regarding good coding standards and readability. 
fun main(arg: Array<String>) {

    //do while user guess ! = Mersenne Prime. 
    do {
        //initializing variable
        var number: Int = 3
        try {
            number = readLine()!!.toInt()

            if (isMersennePrime(number)) 
            println("${number} is a Mersenne Prime.  Congratulations.") 

            else 
            println("${number} is not a Mersenne Prime.") 
        }
        catch (e: NumberFormatException) {
            println(" is not a valid number.  Exiting.") 
        }
    } while (! isMersennePrime(number))
}

    // is Number both prime and 2^n - 1?  
    fun isMersennePrime(Number: Int): Boolean =    
    (twonminus1(Number.toDouble()) && isPrime(Number))

    // is x Prime? 
    fun isPrime(x: Int): Boolean = (2..x-1).all{x % it ! = 0 && x ! = 2}

    // is x = 2^n - 1? 
    fun twonminus1(x: Double): Boolean = Math.log(x + 1.0)/Math.log(2.0) % 1.0 == 0.0

A:

Others already made some good points.   Calling isMersennePrime twice is really bad because that can be very computationally intensive. 
I'm not sure why you are not allowing 2 to be a prime number.   Where I'm from 2 is prime. 
When scanning for primes, you can stop at sqrt(x) instead of x - 1.   If y * z = x, one of y or z is smaller than sqrt(x). 
@Roland gave you a trick on checking if an integer is a power of two, but I just wanted to add a reference to wikipedia with some explanation. 
Also var number: Int = 3 is quite odd.   It's better to use immutable val.  Instead:
while (true) {
    print("Enter a number: ")
    val text = readLine()
    val number = try {
        text!!.toInt()
    } catch (e: NumberFormatException) {
        println("$text is not a valid number.  Exiting.") 
        break
    }
    if (isMersennePrime(number)) {
        println("${number} is a Mersenne Prime.  Congratulations.   Exiting.") 
        break
    } else {
        println("${number} is not a Mersenne Prime.   Try again.") 
    }
}

