Inspried by Satyajit Mohanty

Computer Science Level 4

Let $S$ be the set of numbers less than $5$ billions and can be expressed in the form $n^2+5n+23$ , where $n$ is a positive integer.

Let $N$ be the smallest prime number that divides for some elements of $S$ .

Let $p$ be the number of elements of $S$ that are prime.

Let $q$ be the number of elements of $S$ that are divisible by $N$ .

Find $N+p+q$ .

Inspiration .

The answer is 19663.

1 solution

Pranjal Jain
Mar 30, 2016

from sympy import isprime
S=set()
i=1
def f(n):
    return n*n+5*n+23
while True:
    x=f(i)
    if x>=5*10**9:
        break
    S.add(x)
    i+=1
N=29    #for n=1, f(n)=29 which is prime
p=sum(1 for i in S if isprime(i))
q=sum(1 for i in S if i%N==0)
print(N+p+q)   #Prints 19663

Inspried by Satyajit Mohanty

The answer is 19663.

1 solution

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