Nested prime function

Computer Science Level 3

Let p n p_n denote the n th n^\text{th} prime number , then the following equations are true.

p 1 = 2 p p 1 = 3 p p p 1 = 5 \begin{aligned} p_1 &= & 2 \\ p_{p_1} &= & 3 \\ p_{p_{p_1}} &= & 5 \\ \end{aligned}

Find the value of N N such that p p p p p ⋅ ⋅ ⋅ 1 ⏟ number of p ’s = N = 648391 \large \underbrace{p_{p_{p_{p_{p_{\cdot_{\cdot_{\cdot_1}}}}}}}}_{\text{number of }p\text{'s} =N} = 648391 .


The answer is 10.

Pi Han Goh by Pi Han Goh , 30, Malaysia

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1 solution

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Mar 2, 2017 
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bool prime ;
int primes[1000000] ; int count = 3 ; //start for primes array
primes[0] = 2 ; primes[1] = 3 ; primes[2] = 5 ; primes[3] = 7 ;

for(int i = 11 ; ; i += 2){ //create possible primes
     prime = true ;
     for(int a = 3 ; a <= sqrt(i) ; a += 2) if(i%a == 0){ //check relevant factors
             prime = false ;
             break ;
    }
    if(prime){
         count ++ ;
         primes[count] = i ;
         if(i == 648391) break ; 
    }  
}
int value = 1 ;  
count = 0 ;
while(value != 648391){ //loop through cases of Nth prime
     value = primes[value-1] ;
     count ++ ;
}
cout << count ;

As well, the Nth prime could be generated on demand, overall being a better/smarter method, but this works fine for such a problem.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Yayyyyyy!!!!

Pi Han Goh - 4 years, 3 months ago

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