PRIME_NUMBER_GENERATION_TWO
The Python program featured in this tutorial web page instantiates a dynamic array of N int-type elements and populates that array with the first N prime numbers in ascending order (where the first element of that array is 2). The program uses an algorithm named the Sieve of Eratosthenes to generate those prime numbers.
The Python program file which is featured in this tutorial web page has many common attributes with the C++ source code file featured on the tutorial web page of this website named PRIME_NUMBER_GENERATION. Unlike that C++ source code file, this Python program generates slightly different output messages (to the command line terminal and to the generated and/or overwritten output file).
A prime number is a natural number which is larger than or equal to 2 and which is the multiplicative product of only itself and 1.
A composite number is a natural number which is larger than 1 and which is the multiplicative product of two or more prime numbers.
To view hidden text inside each of the preformatted text boxes below, scroll horizontally.
SOFTWARE_APPLICATION_COMPONENTS
python_source_file: https://raw.githubusercontent.com/karlinarayberinger/KARLINA_OBJECT_extension_pack_22/main/prime_numbers_generation.py
plain_text_file: https://raw.githubusercontent.com/karlinarayberinger/KARLINA_OBJECT_extension_pack_21/main/prime_numbers_generation_output_two.txt
PROGRAM_INTERPRETATION_AND_EXECUTION
STEP_0: Copy and paste the Python source code into a new text editor document and save that document as the following file name:
prime_numbers_generation.py
STEP_1: Open a Unix command line terminal application and set the current directory to wherever the C++ is located on the local machine (e.g. Desktop).
cd Desktop
STEP_2: Run the program by entering the following command:
python3 prime_numbers_generation.py
STEP_3: If the program interpretation command does not work, then use the following commands (in top-down order) to install the Python interpreter:
sudo apt update
sudo apt install python3
STEP_4: After running the Python program is booted up, the following prompt will appear:
Enter the number of prime numbers to generate (N):
STEP_5: Enter a value for a using the keyboard.
STEP_6: Observe program results on the command line terminal and in the output file.
PROGRAM_SOURCE_CODE
The text in the preformatted text box below appears on this web page (while rendered correctly by the web browser) to be identical to the content of the Python source code file whose Uniform Resource Locator is displayed in the green hyperlink below.
Note that, unlike C++ program files (which are compiled into machine-executable instructions before program runtime), Python program files are interpreted one line at a time instead.
python_source_file: https://raw.githubusercontent.com/karlinarayberinger/KARLINA_OBJECT_extension_pack_22/main/prime_numbers_generation.py
#########################################################################################
# file: prime_numbers_generation.py
# type: Python
# date: 05_OCTOBER_2024
# author: karbytes
# license: PUBLIC_DOMAIN
#########################################################################################
import math # math.log(), math.sqrt() # Note that the math.log() is the natural logarithm
def generate_primes(N):
"""Generate an array of the first N prime numbers using the Sieve of Eratosthenes algorithm."""
# Validate the function input and correct that input if it is determined to be an "out of range" value.
if N < 1 or N > 10000:
N = 10
# Calculate an upper limit for the sieve
limit = 15 if N < 6 else int(N * math.log(N) + N * math.log(math.log(N)))
# Create a boolean array "is_prime[0..limit]" and initialize all entries as true.
is_prime = [True] * (limit + 1)
is_prime[0] = is_prime[1] = False # 0 and 1 are not prime numbers.
# Use the Sieve of Eratosthenes.
for p in range(2, int(math.sqrt(limit)) + 1):
if is_prime[p]:
for i in range(p * p, limit + 1, p):
is_prime[i] = False
# Collect the first N primes.
primes = []
count = 0
for p in range(2, limit + 1):
if is_prime[p]:
primes.append(p)
count += 1
if count == N:
break
return primes
def main():
# Declare and initialize the number of primes to generate.
N = 1
# Declare an empty array to store the first N primes.
A = []
# Open the output file for writing
with open("prime_numbers_generation_output.txt", "w") as file:
# Print an opening message to the command line terminal.
print("\n\n--------------------------------")
print("Start Of Program")
print("--------------------------------")
# Print an opening message to the output file.
file.write("--------------------------------\n")
file.write("Start Of Program\n")
file.write("--------------------------------\n")
# Print "This Python program generates the first N prime numbers using an algorithm named the Sieve of Eratosthenes." to the command line terminal and to the output file.
print("\n\nThis Python program generates the first N prime numbers using an algorithm named the Sieve of Eratosthenes.")
file.write("\n\nThis Python program generates the first N prime numbers using an algorithm named the Sieve of Eratosthenes.")
# Print a horizontal divider line to the command line terminal and to the output file.
print("\n\n--------------------------------")
file.write("\n\n--------------------------------")
# Get user input for the number of primes to generate
N = int(input("\n\nEnter the number of prime numbers to generate (N): "))
# Log user input to the file after it is entered.
file.write(f"\n\nEntered value: N = {N}")
print(f"\n\nEntered value: N = {N}")
# Print a horizontal divider line to the command line terminal and to the output file.
print("\n\n--------------------------------")
file.write("\n\n--------------------------------")
# Execute the prime number generation function
A = generate_primes(N)
# Print each element of A to the command line terminal and to the output file.
for i in range(len(A)):
print(f"\n\nA[{i}] := {A[i]}.")
file.write(f"\n\nA[{i}] := {A[i]}.")
# Print a closing message to the command line terminal.
print("\n\n--------------------------------")
print("End Of Program")
print("--------------------------------\n\n")
# Print a closing message to the output file.
file.write("\n\n--------------------------------\n")
file.write("End Of Program\n")
file.write("--------------------------------\n")
# Program entry point
if __name__ == "__main__":
main()
SAMPLE_PROGRAM_OUTPUT
The text in the preformatted text box below was generated by one use case of the Python program featured in this computer programming tutorial web page.
(Note that the aforementioned Python program specifies to name the output file prime_numbers_generation_output.txt instead of prime_numbers_generation_output_two.txt (which is what the hyperlinked plain-text file below is named) because karbytes did not want the C++ program’s output file (which is named prime_numbers_generation_output.txt) to be overwritten with the Python program output file in the GitHub repository which houses both output files and which is named KARLINA_OBJECT_extension_pack_21).
plain_text_file: https://raw.githubusercontent.com/karlinarayberinger/KARLINA_OBJECT_extension_pack_21/main/prime_numbers_generation_output_two.txt
-------------------------------- Start Of Program -------------------------------- This Python program generates the first N prime numbers using an algorithm named the Sieve of Eratosthenes. -------------------------------- Entered value: N = 100 -------------------------------- A[0] := 2. A[1] := 3. A[2] := 5. A[3] := 7. A[4] := 11. A[5] := 13. A[6] := 17. A[7] := 19. A[8] := 23. A[9] := 29. A[10] := 31. A[11] := 37. A[12] := 41. A[13] := 43. A[14] := 47. A[15] := 53. A[16] := 59. A[17] := 61. A[18] := 67. A[19] := 71. A[20] := 73. A[21] := 79. A[22] := 83. A[23] := 89. A[24] := 97. A[25] := 101. A[26] := 103. A[27] := 107. A[28] := 109. A[29] := 113. A[30] := 127. A[31] := 131. A[32] := 137. A[33] := 139. A[34] := 149. A[35] := 151. A[36] := 157. A[37] := 163. A[38] := 167. A[39] := 173. A[40] := 179. A[41] := 181. A[42] := 191. A[43] := 193. A[44] := 197. A[45] := 199. A[46] := 211. A[47] := 223. A[48] := 227. A[49] := 229. A[50] := 233. A[51] := 239. A[52] := 241. A[53] := 251. A[54] := 257. A[55] := 263. A[56] := 269. A[57] := 271. A[58] := 277. A[59] := 281. A[60] := 283. A[61] := 293. A[62] := 307. A[63] := 311. A[64] := 313. A[65] := 317. A[66] := 331. A[67] := 337. A[68] := 347. A[69] := 349. A[70] := 353. A[71] := 359. A[72] := 367. A[73] := 373. A[74] := 379. A[75] := 383. A[76] := 389. A[77] := 397. A[78] := 401. A[79] := 409. A[80] := 419. A[81] := 421. A[82] := 431. A[83] := 433. A[84] := 439. A[85] := 443. A[86] := 449. A[87] := 457. A[88] := 461. A[89] := 463. A[90] := 467. A[91] := 479. A[92] := 487. A[93] := 491. A[94] := 499. A[95] := 503. A[96] := 509. A[97] := 521. A[98] := 523. A[99] := 541. -------------------------------- End Of Program --------------------------------
This web page was last updated on 05_OCTOBER_2024. The content displayed on this web page is licensed as PUBLIC_DOMAIN intellectual property.