What is the optimal time complexity of solving Can a number be expressed as a sum of two prime numbers?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Can a number be expressed as a sum of two prime numbers?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Can a number be expressed as a sum of two prime numbers?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Can a number be expressed as a sum of two prime numbers?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Can a number be expressed as a sum of two prime numbers

Learn how to solve the 'Can a number be expressed as a sum of two prime numbers' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function is_sum_of_two_primes(n) that takes a positive integer n and returns True if n can be expressed as the sum of two prime numbers, and False otherwise.

For example, 10 = 3 + 7 (both prime), so it returns True. Check all possible pairs (p, n-p) where p is prime and n-p is also prime.

Constraints

•2 <= n <= 10^4

Examples

Example 1

Input

is_sum_of_two_primes(10)

Output

True

Explanation

10 = 3 + 7. Both 3 and 7 are prime, so True.

Example 2

Input

is_sum_of_two_primes(11)

Output

True

Explanation

11 = 2 + 9? No (9 not prime). 11 = 3 + 8? No. 11 = 5 + 6? No. But wait — we only need one valid pair. Since all fail here... Actually: no valid pair exists with distinct primes, but wait: is_sum_of_two_primes should be False for 11? Let's check: 2+9=11(9 not prime), 3+8(8 not prime), 5+6(6 not prime). Actually False.

Example 3

Input

is_sum_of_two_primes(4)

Output

True

Explanation

4 = 2 + 2. Both are prime, so True.

Need a Hint?

Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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