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# Task 1 - Your task is to create a Python function, is_prime(n), that determines whether a given number n is prime. This function should return either True or False.

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import math

# math module allows you to use mathematical functions such as trigonometric functions (sin, cos, tan), log functions, constants (math.pi), and math operations (math.sqrt)

def is_prime(n):

    # Lowest prime numbers are 2 and 3, 1 is not considered a prime
    if n < 2:
        return False

    if n == 2 or n == 3:
        return True

    # Check for divisibility from 2 to the square root of n
    # Why sqrt of n? Because every combination past that is just a mirrored repetition of the factors before the sqrt --> 2*17 and 17*2. If n is not a prime number and has a factor greater than the sqrt, then it also has a factor lower than the sqrta

    for i in range(2, int(math.sqrt(n)) + 1):
        if n % i == 0:
            return False

    # % returns the remainder. If value is 0, n is divisible by i and not a prime number
    # Remainder is >0 and not divisible by 2 to sqrt(n)
    return True

# Tester
number = 89
print(f"{number} is prime: {is_prime(number)}")



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# Task 2 - After creating a function to check if a number is prime, consider the range of natural numbers from 100 to 151 inclusive. Find how many prime numbers are present in this range.

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def count_primes(lower, upper):

    prime_count = 0

    for num in range(lower, upper + 1):
        if is_prime(num):
            prime_count += 1
    return prime_count

# Range:
lower_bound = 100
upper_bound = 151
num_primes = count_primes(lower_bound, upper_bound)
print(f"Number of prime numbers between {lower_bound} and {upper_bound}: {num_primes}")