PRIME PERMUTATIONS P ≤ 5 ( MODULO 6)

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import sympy

from tkinter import *

from tkinter import messagebox

# Function to generate and display the prime factorizations of composite numbers

def generate_factorizations():

# Get the custom limit from the input box

limit = int(limit_input.get())

# Generate all the composite numbers congruent to 1, 5, and 7 modulo 6 up to the custom limit

nums = []

for n in range(25, limit + 1):

if n % 6 in (1, 5, 7, 11) and not sympy.isprime(n):

nums.append(n)

# Generate the prime factorization of each composite number

factorizations = {}

for n in nums:

factorizations[n] = sympy.factorint(n)

# Clear the existing output text and display the factorizations in the desired format

output_text.delete('1.0', END)

for n, factors in factorizations.items():

output_text.insert(END, f"{n} = {' x '.join(str(p) + '^' + str(e) for p, e in factors.items())}\n")

# Check if all the factors are prime numbers

all_primes = all(all(sympy.isprime(p) for p in factors.keys()) for factors in factorizations.values())

# Display a message box with the result

if all_primes:

messagebox.showinfo("All prime factors", "All factors in the output are prime numbers.")

else:

messagebox.showwarning("Not all prime factors", "Some factors in the output are not prime numbers.")

# Create the main window and widgets

root = Tk()

root.title("Prime Factorization Generator P ≡ 1, 5, 7, 11 MOD 6")

limit_label = Label(root, text="Enter a limit:")

limit_label.grid(row=0, column=0)

limit_input = Entry(root)

limit_input.grid(row=0, column=1)

generate_button = Button(root, text="Generate Factorizations", command=generate_factorizations)

generate_button.grid(row=1, column=0, columnspan=2)

output_label = Label(root, text="Prime factorizations:")

output_label.grid(row=2, column=0)

output_text = Text(root, height=20, width=50)

output_text.grid(row=3, column=0, columnspan=2)

root.mainloop()