Think of the number guessing game: the smart strategy is to guess the middle, and each "higher" or "lower" rules out half of the remaining numbers. From 1 to 100 you never need more than 7 guesses.

Binary search does that on a sorted list. Keep track of the range where the target could be, from low to high. Look at the middle item: if it's the target, done; if it's too small, the target must be in the upper half; if too big, the lower half. Repeat until found, or until the range is empty.

def binary_search(items, target):
    low = 0
    high = len(items) - 1
    while low <= high:
        mid = (low + high) // 2
        if items[mid] == target:
            return mid
        elif items[mid] < target:
            low = mid + 1
        else:
            high = mid - 1
    return -1

primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]
print(binary_search(primes, 23))
print(binary_search(primes, 4))