Prime numbers in Ranges

'''
CHAPTER 1
'''

def isPrime(n):
    if n < 0 or int(n) != n:
        return None
    if n == 2:
        return True
    if n == 1 or n % 2 == 0:
        return False
    elif n % 2 == 1:
        flag = True
        for i in range(2, int(n/3)+1):
            if n % i == 0:
                flag = False
                return flag
        if flag:
            return flag

# This function will calculate how many prime numbers are in the range [10^a, 10^b)
def howManyPrimes(a, b):
    if a < 0 or b < 0 or a != int(a) or b != int(b):
        return None
    primes = []
    for i in range(10**a, 10**b):
        if isPrime(i):
            primes.append(i)
    return len(primes)


'''
CHAPTER 2
'''

# MAIN FUNCTION
# Basic Data
limitPowerOf10 = 4

# First, I want to show how many primes are in each specific logarithmic range
# List 1
primesInContinuousRanges = []
for i in range(0, limitPowerOf10):
    primesInContinuousRanges.append(howManyPrimes(i, i+1))
print()

xlabels = []
for i in range(0, limitPowerOf10):
    string1 = str(10**i) + "-" + str(10**(i+1))
    xlabels.append(string1)
print("~~~~~~~~ Data 1 ~~~~~~~~")
for i in range(0, len(primesInContinuousRanges)):
    print("There are " + str(primesInContinuousRanges[i]) + " primes in range " + xlabels[i])
print()

# Now, I have to find how many primes are in the range [1, 10^x]
# List 2
primesInWholeRanges = []
for i in range(0, len(primesInContinuousRanges)):
    primesInWholeRanges.append(sum(primesInContinuousRanges[0:i+1]))

xlabels2 = []
for i in range(0, limitPowerOf10):
    string1 = str(1) + "-" + str(10**(i+1))
    xlabels2.append(string1)
print("~~~~~~~~ Data 2 ~~~~~~~~")
for i in range(0, len(primesInWholeRanges)):
    print("There are " + str(primesInWholeRanges[i]) + " primes in range " + xlabels2[i])
print()

# List 3
# Last step is to calculate the appearance frequency of a prime in a whole range
frequencies = []
for i in range(len(primesInWholeRanges)):
    frequencies.append(10**(i+1) / primesInWholeRanges[i])
print("~~~~~~~~ Data 3 ~~~~~~~~")
for i in range(len(frequencies)):
    print("You can find 1 prime number out of " + str(frequencies[i]) + " single numbers in the range " + xlabels2[i])
print()

'''
CHAPTER 3
'''
import matplotlib.pyplot as plt
plt.plot(xlabels, primesInContinuousRanges, 'o', label="Primes in specific range")
plt.xlabel("Ranges in logarithmic scale")
plt.ylabel("Number of primes in each range")
plt.show()

plt.plot(xlabels2, primesInWholeRanges, 'o', label="Primes in a whole range")
plt.xlabel("Ranges in logarithmic scale")
plt.ylabel("Number of primes in a whole range")
plt.show()

plt.plot(xlabels2, frequencies, 'r--', label="Appearance Frequency")
plt.xlabel("Ranges in logarithmic scale")
plt.ylabel("Appearance frequency of a prime in a whole range")
plt.show()