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Illegal prime numbers

+2 votes
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it is illegal to share some certain prime numbers in US and if you do so,you will get arrested.Follow this link to get more details :

My question is : it is very easy to find multiplication of two prime numbers but tough to get what are the prime numbers which multiplication results this number . Example : 7*11= 77 but you are given 77 = ? * ? where ?= two prime numbers only (ans = 7 and 11).Another example : 11*13= 143 but you need to solve it for 143 and you output : 11 13
So I need a program ,efficient one, to get solutions to such type of mathematical problem.
Adding more examples:
input:1. 21 -> 3,7
2. 189 -> 3,7,9
3.1363 -> 29,47 .... and if is not possible then print -1 example 1. 4 and its factors 2*2 where 2 is repeated so print -1
2. 9-> -1
3. 24->-1 ( prime factors are 2^3 * 3= 8*3 where 8 is not prime so print -1).
Thanks in advance.

posted Jul 5, 2016 by Shivam Kumar Pandey

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1 Answer

+5 votes
 
Best answer

This is an interesting topic!

To check if a number is prime number, we have to divide it with all the numerical values between 2 and the number it self and check for reminder.

Typical implementation,

boolean isPrimeNumber(long number) {
    for(int i=2; i<number; i++) {
        if(number % i == 0)
            return false;
    }
    return true;
}

Possible optimizations....
- We don't have to iterate more than half of the number while even, you know if the value is more than half then multiplying it by two will lead to more than what we want.
- We don't have to iterate more than 1/3rd of the number while odd, assuming to be divisible by 3.
Optimized implementation,

static boolean isPrimeNumber(float number) {
    float iterateTill = 0;
    if(number%1 != 0) {
        return false;
    }
    if (number%2 == 0) {
         iterateTill = number/2;
    }
    else {
         iterateTill = number/3;
    }
    for(int i=2; i<=iterateTill; i++) {
        if(number % i == 0)
            return false;
    }
    return true;
}

I will think over this and if I find any better solution, I will post it.

Hope this helps!

Update 1:

Sorry for not understanding the question thoroughly! This method prints the result you seek. Assuming there could be more than 2 prime numbers multiplied in the provided number. I will refine the code further....

static boolean getPrimeNumbersWithin(long number) {
    long firstNumber = 2;
    long secondNumber = 2;
    float remainingNumber = number;

    while(remainingNumber > 0 && firstNumber < number) {
        remainingNumber = (float)number/(float)firstNumber;
        if(isWholeNumber(remainingNumber)) {
            if(isPrimeNumber(remainingNumber)) {
                secondNumber = (long)remainingNumber;
                remainingNumber = 0;
                break;
            }
            else {
                // try if this could be acheived with more numbers
                if (getPrimeNumbersWithin((long)remainingNumber)) {
                    secondNumber = 0;
                    remainingNumber = 0;
                    break;
                }
            }
        }
        do {
            firstNumber++;
        }
        while(!isPrimeNumber(firstNumber));
    }
    if(remainingNumber == 0) {
        System.out.println(firstNumber);
        if(secondNumber != 0){
            System.out.println(secondNumber);
        }
        return true;
    }
    else {
        System.out.println("No match");
        return false;
    }
}

static boolean isWholeNumber(float number) {
    if(number%1 != 0) {
        return false;
    }
    return true;
}

Test run result,

getPrimeNumbersWithin(6090); // Results 7 29 5 3 2

online link for your immediate reference.

answer Jul 6, 2016 by Vinod Kumar K V
I think checking till SQRT(n) should be fine...
But the problem is not to check if number is prime or not, but to find out the prime factors of a number. Do you like to correct your solution?
Hi Vinod,your solution isn't according to problem.
Adding more examples:
input:1. 21 -> 3,7
2. 189 -> 3,7,9
3.1363 -> 29,47 .... and if is not possible then print -1 example 1. 4 and its factors 2*2 where 2*2=4 is is not prime so print -1
2. 9-> -1
3. 24->-1 ( prime factors are 2^3 * 3= 8*3 where 8 is not prime so print -1).
Oh! Sorry, my bad. I will update my answer.
ok @Vinod
Thanks Vinod, I just checked the solution with various inputs like 144: 3 3 2 2 2 2( it should be -1 only ) but it doesn't matter as we are getting good results for other inputs like 10010 ...etc. gave you +1
Thank you @Shivam
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