2523. Closest Prime Numbers in Range

Given two positive integers left and right, find the two integers num1 and num2 such that:

• left <= num1 < num2 <= right .
• Both num1 and num2 are prime numbers.
• num2 - num1 is the minimum amongst all other pairs satisfying the above conditions.

Return the positive integer array ans = [num1, num2]. If there are multiple pairs satisfying these conditions, return the one with the smallest num1 value. If no such numbers exist, return [-1, -1].

Example 1:

Input: left = 10, right = 19
Output: [11,13]
Explanation: The prime numbers between 10 and 19 are 11, 13, 17, and 19.
The closest gap between any pair is 2, which can be achieved by [11,13] or [17,19].
Since 11 is smaller than 17, we return the first pair.

Example 2:

Input: left = 4, right = 6
Output: [-1,-1]
Explanation: There exists only one prime number in the given range, so the conditions cannot be satisfied.

def isPrime(self, num):
	if num < 2:
		return False
	if num == 2 or num == 3:
		return True
	if num % 2 == 0:
		return False
	divisor = 3
	while divisor * divisor <= num:
		if num % divisor == 0:
			return False
		divisor += 2
	return True
def closestPrimes(self, left: int, right: int) -> List[int]:
	prev_prime = -1
	closestA = -1
	closestB = -1
	min_difference = float("inf")

	# Iterate over the range of numbers and find primes
	for candidate in range(left, right + 1):
		if self.isPrime(candidate):
			if prev_prime != -1:
				difference = candidate - prev_prime
				if difference < min_difference:
					min_difference = difference
					closestA = prev_prime
					closestB = candidate
				if difference == 1 or difference == 2:
					return [prev_prime, candidate]
			prev_prime = candidate

	return [closestA, closestB] if closestA != -1 else [-1, -1]