| 8 | 8 | * @returns {number} |
| 9 | 9 | */ |
| 10 | 10 | export const prime = (ordinal) => { |
| 11 | | throw new Error('Remove this line and implement the function'); |
| 11 | // Edge Case: Invalid input - zero |
| 12 | if (ordinal === 0) { |
| 13 | throw new Error('there is no zeroth prime'); |
| 14 | } |
| 15 | |
| 16 | // Edge Case: Invalid input - negative number |
| 17 | if (ordinal < 0) { |
| 18 | throw new Error('prime number index must be positive'); |
| 19 | } |
| 20 | |
| 21 | // Edge Case: Invalid input - non-integer |
| 22 | if (!Number.isInteger(ordinal)) { |
| 23 | throw new Error('prime number index must be an integer'); |
| 24 | } |
| 25 | |
| 26 | // Edge Case: First prime number |
| 27 | if (ordinal === 1) { |
| 28 | return 2; |
| 29 | } |
| 30 | |
| 31 | let count = 1; // We already know 2 is prime |
| 32 | let candidate = 1; // Start checking from 3 (first odd number after 2) |
| 33 | |
| 34 | while (count < ordinal) { |
| 35 | candidate += 2; // Only check odd numbers |
| 36 | if (isPrime(candidate)) { |
| 37 | count++; |
| 38 | } |
| 39 | } |
| 40 | |
| 41 | return candidate; |
| 12 | 42 | }; |
| 43 | |
| 44 | /** |
| 45 | * Helper function to check if a number is prime |
| 46 | * @param {number} num |
| 47 | * @returns {boolean} |
| 48 | */ |
| 49 | function isPrime(num) { |
| 50 | // Edge Case: Numbers less than 2 are not prime |
| 51 | if (num < 2) { |
| 52 | return false; |
| 53 | } |
| 54 | |
| 55 | // Edge Case: 2 is prime |
| 56 | if (num === 2) { |
| 57 | return true; |
| 58 | } |
| 59 | |
| 60 | // Edge Case: Even numbers greater than 2 are not prime |
| 61 | if (num % 2 === 0) { |
| 62 | return false; |
| 63 | } |
| 64 | |
| 65 | // Check odd divisors up to square root of num |
| 66 | const sqrt = Math.sqrt(num); |
| 67 | for (let i = 3; i <= sqrt; i += 2) { |
| 68 | if (num % i === 0) { |
| 69 | return false; |
| 70 | } |
| 71 | } |
| 72 | |
| 73 | return true; |
| 74 | } |
| 75 | |
| 76 | // Handled Edge Cases: ordinal is 0, ordinal is negative, ordinal is non-integer, ordinal is 1, num is less than 2, num is 2, num is even and greater than 2 |