Prime Fibonacci? Sounds Crazy!

Java code :

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long stime = System.currentTimeMillis() ;
    int i = 0,sum=0,j=1 ;
    for(;j<1000000000;){
    i=i+j ;
    j=i+j ;
    if(isprime(i))
       {if(isprime(j))
            sum=sum+i+j ;
        else
            sum=sum+i ;}
    else
        {if(isprime(j))
            sum=sum+j ;}
    }
    System.out.print(sum) ;
    long etime = System.currentTimeMillis() ;
    long time = etime-stime ;
    System.out.print(",Time taken is "+time+"ms");

Also I have created a method called isprime which tests whether a number is prime or not. It's code is as follows.

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 public static boolean isprime(long n){
   if(n==2)
       return true ;  // checking whether the number is 2 or not
   else        // else 1
      {if(n==1)
          return false ; // checking whether the number is 1 or not
       else  // else 2
         {int k = (int) Math.pow(n,0.5) ;  // taking square root of number
          if(n%2==0)
          return false ;
          else      //else 3
             {for(int s=3;s<k+1;s=s+2){
              if(n%s==0)   // checking by dividing against all odd numbers
              return false ;} // bracket of for loop
              return true ;}  // bracket of else 3

         } //brakcet of else 2
       }  // brakcet of else 1
   } // bracket of method 

The result appended is as follows :

1

434039265,Time taken is 1ms

Just like all other problems of this set, make a list in python, and then operate the list. img

We see that in the list, some directly seen primes are $2,3,5,13,89$

For the other ones, we'll try factorizing the suspicable elements of the list, i.e. those who are not even, or end with 5 , not divisible by 3.

I used $GeoGebra$ for factorizing the numbers.

We get Prime factorizations of the numbers as $\displaystyle 89=\textbf{prime}\\ 233=\textbf{prime}\\ 377=13\times 29 \\987=\textbf{divisible by 3}\\ 1597=\textbf{prime}\\ 4181=37\times 113\\ 17711=89\times 199\\ 28657=\textbf{prime}\\ 121393=233\times 521 \\ 317811=3\times 13\times 29\times 281 \\514229=\textbf{prime}\\ 1346269=557\times 2417 \\2178309=\textbf{divisible by 3}\\ 5702887=1597\times 3571 \\24157817=73\times 149\times 2221 \\39088169=37\times 113 \times 9349\\165580141=2789\times 59369\\ 433494437=\textbf{prime}\\ 701408733=\textbf{divisible by 3}$

Sum of all the primes is $2+3+5+13+89+233+1597+28657+514229+433494437 =\boxed{434039265}$

Here's my C++ code

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#include<iostream>
#include<cmath>
#define num 1000000000
using namespace std;
bool checkPrime(long long int n)
{
    if(n==1)
        return false;
    long long int i=sqrt(n);
    for(;i>=2;i--)
    {
        if(n%i==0)
            return false;
    }
    return true;
}
int main()
{
    unsigned long long int a=0,b=1,sum=0,c;
    c=a+b;
    while(c<=num)
    {
        if(checkPrime(c))
            sum+=c;
        a=b;
        b=c;
        c=a+b;
    }
    cout<<sum;
    return 0;
}

In Java

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import java.math.BigInteger;
public class main {  
  public static void main (String[] args) {
      BigInteger a = new BigInteger("1");
      BigInteger b = new BigInteger("1");
      BigInteger c;
      BigInteger Sum = BigInteger.ZERO;
      while (b.compareTo(new BigInteger("1000000000"))==-1){
          c = a.add(b);  a = b ;  b = c;
          if (b.isProbablePrime(10))
              Sum = Sum.add(b);  
      }
      System.out.println(Sum);
     }  
}    

Another colourful solution:

Java solution -

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 public static void main(String args[]){
    double a = 2, b = 3, sum = 0; 
    final double bil = 1_000_000_000;
    do{
        a += b; b += a;
        if( prime(a) ) sum += a;
        if( prime(b) ) sum += b;
    }while(a < bil && b < bil);
    System.out.println(sum + 2 + 3); 
}

static boolean prime(double n) {
    if (n%2==0) return false;
    for(int i=3;i*i<=n;i+=2)
        if(n%i==0) return false;
    return true;
} 

Execution time - 0.001983184 seconds

Conditions

Numbers must be in Fibonacci series Fibonacci series should not go beyond 1 billion The sum should be calculated only for numbers that are prime

C# Program

using System; using System.Collections.Generic; using System.Linq; using System.Text;

namespace ConsoleApplication2 { class Program { static void Main(string[] args) { int sum,a,b,c,f; a=1; b=1; sum =0; c = a + b; while(c<1000000000) { c=a+b; f=0; for (int j = 2; j < (c / 2); j++) { if (c % j == 0) { f = 1; break; } }

            if (f == 0)
            { sum = sum + c; }
            a = b;
            b = c;

        }

        Console.WriteLine("sum is "+sum);
        Console.ReadLine();
            }



}

}

Using Java:

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public class value {
    static boolean isprime(int x)
    {
        boolean t=true;
        for(int i=2;i<Math.sqrt(x);i++)
        {
            if(x%i==0){
                t=false;
                break;
            }else
                t=true;
        }

        return t;
    }
    public static void main(String[] args) {
        int f1=1,f2=1;
        int sum=0;

        int fn=f1+f2;
        for(;fn<1000000000;)
        {
            if(isprime(fn))
            {
                sum+=fn;
            }
            f1=f2;
            f2=fn;
            fn=f1+f2;
        }

        System.out.println("\nThe sum is: "+sum);
    }
} 

java implementation:

public static int crazyfibo() { int sum=0; int a=0,b=1; int c=0;

    for (int i=0;i<45;i++)
    {

        c=a+b;

        if (isPrime(c))
        {
            sum+=c;
        }

        a=b;
        b=c;
    }


    return sum;

}

public static boolean isPrime(int n)
{


        if (n <= 3) {
            return n > 1;
        } else if (n % 2 == 0 || n % 3 == 0) {
            return false;
        } else {
            for (int i = 5; i * i <= n; i += 6) {
                if (n % i == 0 || n % (i + 2) == 0) {
                    return false;
                }
            }
            return true;

    }

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from sympy import fibonacci,isprime
A=[]
i=0
while fibonacci(i)<1000000000:
    if isprime(fibonacci(i)) is True:
        A.append(fibonacci(i))
    i+=1
sum(A)

You must install first sympy as a module in python, You can find it in google. Sympy is an elaborated python module that can solve different kinds of mathematics.

Mathematica code:

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a = 0;
Table[If[PrimeQ[Fibonacci[x]], a = a + Fibonacci[x], o = 1], {x, 1, 
 44}];
Print[a]; 

My cute.... or not so cute java code :

class q2{ public static void main(String as[]){ int a=0; int b=1; int c=0; long sum=0;

for(;c<1000000000;){
    c=a+b;
    if(prime(c)){
        sum=sum+c;
    }
    a=b;
    b=c;
}
System.out.print(sum);

}

public static boolean prime(long no){ if(no==1)return false; if(no==2||no==3||no==3||no==5||no==7)return true; if(no%2==0)return false; if(no%3==0)return false; if(no%5==0)return false; if(no%7==0)return false; long ss=(long)Math.sqrt(no);
for(long i=3;i<ss+1;i=i+2){ if(no%i==0)return false; } return true; }

}