What is the method to sum all prime numbers up to N?
A number theory problem requiring prime generation and summation. It tests Sieve of Eratosthenes or trial division.
Why Interviewers Ask This
This question tests knowledge of prime number algorithms and efficiency. Interviewers want to see if candidates can implement the Sieve of Eratosthenes for better performance compared to checking each number individually. It also checks loop optimization.
How to Answer This Question
Explain generating primes up to N using the Sieve of Eratosthenes for O(N log log N) efficiency. Alternatively, check primality for each number up to N using trial division up to sqrt(i). Sum the identified primes. Discuss trade-offs between space and time.
Key Points to Cover
- Prime generation
- Sieve of Eratosthenes
- Summation loop
- Efficiency comparison
Sample Answer
To sum all prime numbers up to N, I can use the Sieve of Eratosthenes algorithm. I create a boolean array marking non-prime numbers and iterate through multiples of each prime starting from 2. After sieving, I iterate th…
Common Mistakes to Avoid
- Including 1 as a prime
- Incorrect sieve range
- Inefficient primality test
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