Python: Find all integers that are the product of exactly three primes

Last update on December 21 2024 07:44:25 (UTC/GMT +8 hours)

Integers as Product of Three Primes

Write a Python program to find all integers <= 1000 that are the product of exactly three primes. Each integer should be represented as a list of its three prime factors.

Input: 
10
Output:
[[2, 2, 2]]

Input: 
50
Output:
[[2, 2, 2], [2, 2, 3], [2, 2, 5], [2, 2, 7], [2, 2, 11], [2, 3, 2], [2, 3, 3], [2, 3, 5], [2, 3, 7], [2, 5, 2], [2, 5, 3], [2, 5, 5], [2, 7, 2], [2, 7, 3], [2, 11, 2], [3, 2, 2], [3, 2, 3], [3, 2, 5], [3, 2, 7], [3, 3, 2], [3, 3, 3], [3, 3, 5], [3, 5, 2], [3, 5, 3], [3, 7, 2], [5, 2, 2], [5, 2, 3], [5, 2, 5], [5, 3, 2], [5, 3, 3], [5, 5, 2], [7, 2, 2], [7, 2, 3], [7, 3, 2], [11, 2, 2]]

Visual Presentation:

Sample Solution:

Python Code:

# License: https://bit.ly/3oLErEI

# Define a function named 'test' that takes an integer parameter 'n'
def test(n):    
    # Generate a list 'ps' containing all prime numbers less than 'n'
    ps = [p for p in range(2, n) if all(p % sat != 0 for sat in range(2, p))]
    
    # Generate a list of lists containing all integers <= 'n' that are the product of exactly three primes
    return [[p, q, r] for p in ps for q in ps for r in ps if p * q * r <= n]   

# Example 1
n1 = 10
print("Number:", n1)
print("Find all integers <= said number that are the product of exactly three primes:")
print(test(n1))

# Example 2
n2 = 50
print("\nNumber:", n2)
print("Find all integers <= said number that are the product of exactly three primes:")
print(test(n2))

# Example 3
n3 = 1000
print("\nNumber:", n3)
print("Find all integers <= said number that are the product of exactly three primes:")
print(test(n3))

Sample Output:

Number: 10
Find all integers <= said number that are the product of exactly three primes:
[[2, 2, 2]]

Number: 50
Find all integers <= said number that are the product of exactly three primes:
[[2, 2, 2], [2, 2, 3], [2, 2, 5], [2, 2, 7], [2, 2, 11], [2, 3, 2], [2, 3, 3], [2, 3, 5], [2, 3, 7], [2, 5, 2], [2, 5, 3], [2, 5, 5], [2, 7, 2], [2, 7, 3], [2, 11, 2], [3, 2, 2], [3, 2, 3], [3, 2, 5], [3, 2, 7], [3, 3, 2], [3, 3, 3], [3, 3, 5], [3, 5, 2], [3, 5, 3], [3, 7, 2], [5, 2, 2], [5, 2, 3], [5, 2, 5], [5, 3, 2], [5, 3, 3], [5, 5, 2], [7, 2, 2], [7, 2, 3], [7, 3, 2], [11, 2, 2]]

Number: 1000
Find all integers <= said number that are the product of exactly three primes:
[[2, 2, 2], [2, 2, 3], [2, 2, 5], [2, 2, 7], [2, 2, 11], [2, 2, 13], [2, 2, 17], [2, 2, 19], [2, 2, 23], [2, 2, 29], [2, 2, 31], [2, 2, 37], [2, 2, 41], [2, 2, 43], [2, 2, 47], [2, 2, 53], [2, 2, 59], [2, 2, 61], [2, 2, 67], [2, 2, 71], [2, 2, 73], [2, 2, 79], [2, 2, 83], [2, 2, 89], [2, 2, 97], [2, 2, 101], [2, 2, 103], [2, 2, 107], [2, 2, 109], [2, 2, 113], [2, 2, 127], [2, 2, 131], [2, 2, 137], [2, 2, 139], [2, 2, 149], [2, 2, 151], [2, 2, 157], [2, 2, 163], [2, 2, 167], [2, 2, 173], [2, 2, 179], [2, 2, 181], [2, 2, 191], [2, 2, 193], [2, 2, 197], [2, 2, 199], [2, 2, 211], [2, 2, 223], [2, 2, 227], [2, 2, 229], [2, 2, 233], [2, 2, 239], [2, 2, 241], [2, 3, 2], [2, 3, 3], [2, 3, 5], [2, 3, 7], [2, 3, 11], [2, 3, 13], [2, 3, 17], [2, 3, 19], [2, 3, 23], [2, 3, 29], [2, 3, 31], [2, 3, 37], [2, 3, 41], [2, 3, 43], [2, 3, 47], [2, 3, 53], [2, 3, 59], [2, 3, 61], [2, 3, 67], [2, 3, 71], [2, 3, 73], [2, 3, 79], [2, 3, 83], [2, 3, 89], [2, 3, 97], [2, 3, 101], [2, 3, 103], [2, 3, 107], [2, 3, 109], [2, 3, 113], [2, 3, 127], [2, 3, 131], [2, 3, 137], [2, 3, 139], [2, 3, 149], [2, 3, 151], [2, 3, 157], [2, 3, 163], [2, 5, 2], [2, 5, 3], [2, 5, 5], [2, 5, 7], [2, 5, 11], [2, 5, 13], [2, 5, 17], [2, 5, 19], [2, 5, 23], [2, 5, 29], [2, 5, 31], [2, 5, 37], [2, 5, 41], [2, 5, 43], [2, 5, 47], [2, 5, 53], [2, 5, 59], [2, 5, 61], [2, 5, 67], [2, 5, 71], [2, 5, 73], [2, 5, 79], [2, 5, 83], [2, 5, 89], [2, 5, 97], [2, 7, 2], [2, 7, 3], [2, 7, 5], [2, 7, 7], [2, 7, 11], [2, 7, 13], [2, 7, 17], [2, 7, 19], [2, 7, 23], [2, 7, 29], [2, 7, 31], [2, 7, 37], [2, 7, 41], [2, 7, 43], [2, 7, 47], [2, 7, 53], [2, 7, 59], [2, 7, 61], [2, 7, 67], [2, 7, 71], [2, 11, 2], [2, 11, 3], [2, 11, 5], [2, 11, 7], [2, 11, 11], [2, 11, 13], [2, 11, 17], [2, 11, 19], [2, 11, 23], [2, 11, 29], [2, 11, 31], [2, 11, 37], [2, 11, 41], [2, 11, 43], [2, 13, 2], [2, 13, 3], [2, 13, 5], [2, 13, 7], [2, 13, 11], [2, 13, 13], [2, 13, 17], [2, 13, 19], [2, 13, 23], [2, 13, 29], [2, 13, 31], [2, 13, 37], [2, 17, 2], [2, 17, 3], [2, 17, 5], [2, 17, 7], [2, 17, 11], [2, 17, 13], [2, 17, 17], [2, 17, 19], [2, 17, 23], [2, 17, 29], [2, 19, 2], [2, 19, 3], [2, 19, 5], [2, 19, 7], [2, 19, 11], [2, 19, 13], [2, 19, 17], [2, 19, 19], [2, 19, 23], [2, 23, 2], [2, 23, 3], [2, 23, 5], [2, 23, 7], [2, 23, 11], [2, 23, 13], [2, 23, 17], [2, 23, 19], [2, 29, 2], [2, 29, 3], [2, 29, 5], [2, 29, 7], [2, 29, 11], [2, 29, 13], [2, 29, 17], [2, 31, 2], [2, 31, 3], [2, 31, 5], [2, 31, 7], [2, 31, 11], [2, 31, 13], [2, 37, 2], [2, 37, 3], [2, 37, 5], [2, 37, 7], [2, 37, 11], [2, 37, 13], [2, 41, 2], [2, 41, 3], [2, 41, 5], [2, 41, 7], [2, 41, 11], [2, 43, 2], [2, 43, 3], [2, 43, 5], [2, 43, 7], [2, 43, 11], [2, 47, 2], [2, 47, 3], [2, 47, 5], [2, 47, 7], [2, 53, 2], [2, 53, 3], [2, 53, 5], [2, 53, 7], [2, 59, 2], [2, 59, 3], [2, 59, 5], [2, 59, 7], [2, 61, 2], [2, 61, 3], [2, 61, 5], [2, 61, 7], [2, 67, 2], [2, 67, 3], [2, 67, 5], [2, 67, 7], [2, 71, 2], [2, 71, 3], [2, 71, 5], [2, 71, 7], [2, 73, 2], [2, 73, 3], [2, 73, 5], [2, 79, 2], [2, 79, 3], [2, 79, 5], [2, 83, 2], [2, 83, 3], [2, 83, 5], [2, 89, 2], [2, 89, 3], [2, 89, 5], [2, 97, 2], [2, 97, 3], [2, 97, 5], [2, 101, 2], [2, 101, 3], [2, 103, 2], [2, 103, 3], [2, 107, 2], [2, 107, 3], [2, 109, 2], [2, 109, 3], [2, 113, 2], [2, 113, 3], [2, 127, 2], [2, 127, 3], [2, 131, 2], [2, 131, 3], [2, 137, 2], [2, 137, 3], [2, 139, 2], [2, 139, 3], [2, 149, 2], [2, 149, 3], [2, 151, 2], [2, 151, 3], [2, 157, 2], [2, 157, 3], [2, 163, 2], [2, 163, 3], [2, 167, 2], [2, 173, 2], [2, 179, 2], [2, 181, 2], [2, 191, 2], [2, 193, 2], [2, 197, 2], [2, 199, 2], [2, 211, 2], [2, 223, 2], [2, 227, 2], [2, 229, 2], [2, 233, 2], [2, 239, 2], [2, 241, 2], [3, 2, 2], [3, 2, 3], [3, 2, 5], [3, 2, 7], [3, 2, 11], [3, 2, 13], [3, 2, 17], [3, 2, 19], [3, 2, 23], [3, 2, 29], [3, 2, 31], [3, 2, 37], [3, 2, 41], [3, 2, 43], [3, 2, 47], [3, 2, 53], [3, 2, 59], [3, 2, 61], [3, 2, 67], [3, 2, 71], [3, 2, 73], [3, 2, 79], [3, 2, 83], [3, 2, 89], [3, 2, 97], [3, 2, 101], [3, 2, 103], [3, 2, 107], [3, 2, 109], [3, 2, 113], [3, 2, 127], [3, 2, 131], [3, 2, 137], [3, 2, 139], [3, 2, 149], [3, 2, 151], [3, 2, 157], [3, 2, 163], [3, 3, 2], [3, 3, 3], [3, 3, 5], [3, 3, 7], [3, 3, 11], [3, 3, 13], [3, 3, 17], [3, 3, 19], [3, 3, 23], [3, 3, 29], [3, 3, 31], [3, 3, 37], [3, 3, 41], [3, 3, 43], [3, 3, 47], [3, 3, 53], [3, 3, 59], [3, 3, 61], [3, 3, 67], [3, 3, 71], [3, 3, 73], [3, 3, 79], [3, 3, 83], [3, 3, 89], [3, 3, 97], [3, 3, 101], [3, 3, 103], [3, 3, 107], [3, 3, 109], [3, 5, 2], [3, 5, 3], [3, 5, 5], [3, 5, 7], [3, 5, 11], [3, 5, 13], [3, 5, 17], [3, 5, 19], [3, 5, 23], [3, 5, 29], [3, 5, 31], [3, 5, 37], [3, 5, 41], [3, 5, 43], [3, 5, 47], [3, 5, 53], [3, 5, 59], [3, 5, 61], [3, 7, 2], [3, 7, 3], [3, 7, 5], [3, 7, 7], [3, 7, 11], [3, 7, 13], [3, 7, 17], [3, 7, 19], [3, 7, 23], [3, 7, 29], [3, 7, 31], [3, 7, 37], [3, 7, 41], [3, 7, 43], [3, 7, 47], [3, 11, 2], [3, 11, 3], [3, 11, 5], [3, 11, 7], [3, 11, 11], [3, 11, 13], [3, 11, 17], [3, 11, 19], [3, 11, 23], [3, 11, 29], [3, 13, 2], [3, 13, 3], [3, 13, 5], [3, 13, 7], [3, 13, 11], [3, 13, 13], [3, 13, 17], [3, 13, 19], [3, 13, 23], [3, 17, 2], [3, 17, 3], [3, 17, 5], [3, 17, 7], [3, 17, 11], [3, 17, 13], [3, 17, 17], [3, 17, 19], [3, 19, 2], [3, 19, 3], [3, 19, 5], [3, 19, 7], [3, 19, 11], [3, 19, 13], [3, 19, 17], [3, 23, 2], [3, 23, 3], [3, 23, 5], [3, 23, 7], [3, 23, 11], [3, 23, 13], [3, 29, 2], [3, 29, 3], [3, 29, 5], [3, 29, 7], [3, 29, 11], [3, 31, 2], [3, 31, 3], [3, 31, 5], [3, 31, 7], [3, 37, 2], [3, 37, 3], [3, 37, 5], [3, 37, 7], [3, 41, 2], [3, 41, 3], [3, 41, 5], [3, 41, 7], [3, 43, 2], [3, 43, 3], [3, 43, 5], [3, 43, 7], [3, 47, 2], [3, 47, 3], [3, 47, 5], [3, 47, 7], [3, 53, 2], [3, 53, 3], [3, 53, 5], [3, 59, 2], [3, 59, 3], [3, 59, 5], [3, 61, 2], [3, 61, 3], [3, 61, 5], [3, 67, 2], [3, 67, 3], [3, 71, 2], [3, 71, 3], [3, 73, 2], [3, 73, 3], [3, 79, 2], [3, 79, 3], [3, 83, 2], [3, 83, 3], [3, 89, 2], [3, 89, 3], [3, 97, 2], [3, 97, 3], [3, 101, 2], [3, 101, 3], [3, 103, 2], [3, 103, 3], [3, 107, 2], [3, 107, 3], [3, 109, 2], [3, 109, 3], [3, 113, 2], [3, 127, 2], [3, 131, 2], [3, 137, 2], [3, 139, 2], [3, 149, 2], [3, 151, 2], [3, 157, 2], [3, 163, 2], [5, 2, 2], [5, 2, 3], [5, 2, 5], [5, 2, 7], [5, 2, 11], [5, 2, 13], [5, 2, 17], [5, 2, 19], [5, 2, 23], [5, 2, 29], [5, 2, 31], [5, 2, 37], [5, 2, 41], [5, 2, 43], [5, 2, 47], [5, 2, 53], [5, 2, 59], [5, 2, 61], [5, 2, 67], [5, 2, 71], [5, 2, 73], [5, 2, 79], [5, 2, 83], [5, 2, 89], [5, 2, 97], [5, 3, 2], [5, 3, 3], [5, 3, 5], [5, 3, 7], [5, 3, 11], [5, 3, 13], [5, 3, 17], [5, 3, 19], [5, 3, 23], [5, 3, 29], [5, 3, 31], [5, 3, 37], [5, 3, 41], [5, 3, 43], [5, 3, 47], [5, 3, 53], [5, 3, 59], [5, 3, 61], [5, 5, 2], [5, 5, 3], [5, 5, 5], [5, 5, 7], [5, 5, 11], [5, 5, 13], [5, 5, 17], [5, 5, 19], [5, 5, 23], [5, 5, 29], [5, 5, 31], [5, 5, 37], [5, 7, 2], [5, 7, 3], [5, 7, 5], [5, 7, 7], [5, 7, 11], [5, 7, 13], [5, 7, 17], [5, 7, 19], [5, 7, 23], [5, 11, 2], [5, 11, 3], [5, 11, 5], [5, 11, 7], [5, 11, 11], [5, 11, 13], [5, 11, 17], [5, 13, 2], [5, 13, 3], [5, 13, 5], [5, 13, 7], [5, 13, 11], [5, 13, 13], [5, 17, 2], [5, 17, 3], [5, 17, 5], [5, 17, 7], [5, 17, 11], [5, 19, 2], [5, 19, 3], [5, 19, 5], [5, 19, 7], [5, 23, 2], [5, 23, 3], [5, 23, 5], [5, 23, 7], [5, 29, 2], [5, 29, 3], [5, 29, 5], [5, 31, 2], [5, 31, 3], [5, 31, 5], [5, 37, 2], [5, 37, 3], [5, 37, 5], [5, 41, 2], [5, 41, 3], [5, 43, 2], [5, 43, 3], [5, 47, 2], [5, 47, 3], [5, 53, 2], [5, 53, 3], [5, 59, 2], [5, 59, 3], [5, 61, 2], [5, 61, 3], [5, 67, 2], [5, 71, 2], [5, 73, 2], [5, 79, 2], [5, 83, 2], [5, 89, 2], [5, 97, 2], [7, 2, 2], [7, 2, 3], [7, 2, 5], [7, 2, 7], [7, 2, 11], [7, 2, 13], [7, 2, 17], [7, 2, 19], [7, 2, 23], [7, 2, 29], [7, 2, 31], [7, 2, 37], [7, 2, 41], [7, 2, 43], [7, 2, 47], [7, 2, 53], [7, 2, 59], [7, 2, 61], [7, 2, 67], [7, 2, 71], [7, 3, 2], [7, 3, 3], [7, 3, 5], [7, 3, 7], [7, 3, 11], [7, 3, 13], [7, 3, 17], [7, 3, 19], [7, 3, 23], [7, 3, 29], [7, 3, 31], [7, 3, 37], [7, 3, 41], [7, 3, 43], [7, 3, 47], [7, 5, 2], [7, 5, 3], [7, 5, 5], [7, 5, 7], [7, 5, 11], [7, 5, 13], [7, 5, 17], [7, 5, 19], [7, 5, 23], [7, 7, 2], [7, 7, 3], [7, 7, 5], [7, 7, 7], [7, 7, 11], [7, 7, 13], [7, 7, 17], [7, 7, 19], [7, 11, 2], [7, 11, 3], [7, 11, 5], [7, 11, 7], [7, 11, 11], [7, 13, 2], [7, 13, 3], [7, 13, 5], [7, 13, 7], [7, 17, 2], [7, 17, 3], [7, 17, 5], [7, 17, 7], [7, 19, 2], [7, 19, 3], [7, 19, 5], [7, 19, 7], [7, 23, 2], [7, 23, 3], [7, 23, 5], [7, 29, 2], [7, 29, 3], [7, 31, 2], [7, 31, 3], [7, 37, 2], [7, 37, 3], [7, 41, 2], [7, 41, 3], [7, 43, 2], [7, 43, 3], [7, 47, 2], [7, 47, 3], [7, 53, 2], [7, 59, 2], [7, 61, 2], [7, 67, 2], [7, 71, 2], [11, 2, 2], [11, 2, 3], [11, 2, 5], [11, 2, 7], [11, 2, 11], [11, 2, 13], [11, 2, 17], [11, 2, 19], [11, 2, 23], [11, 2, 29], [11, 2, 31], [11, 2, 37], [11, 2, 41], [11, 2, 43], [11, 3, 2], [11, 3, 3], [11, 3, 5], [11, 3, 7], [11, 3, 11], [11, 3, 13], [11, 3, 17], [11, 3, 19], [11, 3, 23], [11, 3, 29], [11, 5, 2], [11, 5, 3], [11, 5, 5], [11, 5, 7], [11, 5, 11], [11, 5, 13], [11, 5, 17], [11, 7, 2], [11, 7, 3], [11, 7, 5], [11, 7, 7], [11, 7, 11], [11, 11, 2], [11, 11, 3], [11, 11, 5], [11, 11, 7], [11, 13, 2], [11, 13, 3], [11, 13, 5], [11, 17, 2], [11, 17, 3], [11, 17, 5], [11, 19, 2], [11, 19, 3], [11, 23, 2], [11, 23, 3], [11, 29, 2], [11, 29, 3], [11, 31, 2], [11, 37, 2], [11, 41, 2], [11, 43, 2], [13, 2, 2], [13, 2, 3], [13, 2, 5], [13, 2, 7], [13, 2, 11], [13, 2, 13], [13, 2, 17], [13, 2, 19], [13, 2, 23], [13, 2, 29], [13, 2, 31], [13, 2, 37], [13, 3, 2], [13, 3, 3], [13, 3, 5], [13, 3, 7], [13, 3, 11], [13, 3, 13], [13, 3, 17], [13, 3, 19], [13, 3, 23], [13, 5, 2], [13, 5, 3], [13, 5, 5], [13, 5, 7], [13, 5, 11], [13, 5, 13], [13, 7, 2], [13, 7, 3], [13, 7, 5], [13, 7, 7], [13, 11, 2], [13, 11, 3], [13, 11, 5], [13, 13, 2], [13, 13, 3], [13, 13, 5], [13, 17, 2], [13, 17, 3], [13, 19, 2], [13, 19, 3], [13, 23, 2], [13, 23, 3], [13, 29, 2], [13, 31, 2], [13, 37, 2], [17, 2, 2], [17, 2, 3], [17, 2, 5], [17, 2, 7], [17, 2, 11], [17, 2, 13], [17, 2, 17], [17, 2, 19], [17, 2, 23], [17, 2, 29], [17, 3, 2], [17, 3, 3], [17, 3, 5], [17, 3, 7], [17, 3, 11], [17, 3, 13], [17, 3, 17], [17, 3, 19], [17, 5, 2], [17, 5, 3], [17, 5, 5], [17, 5, 7], [17, 5, 11], [17, 7, 2], [17, 7, 3], [17, 7, 5], [17, 7, 7], [17, 11, 2], [17, 11, 3], [17, 11, 5], [17, 13, 2], [17, 13, 3], [17, 17, 2], [17, 17, 3], [17, 19, 2], [17, 19, 3], [17, 23, 2], [17, 29, 2], [19, 2, 2], [19, 2, 3], [19, 2, 5], [19, 2, 7], [19, 2, 11], [19, 2, 13], [19, 2, 17], [19, 2, 19], [19, 2, 23], [19, 3, 2], [19, 3, 3], [19, 3, 5], [19, 3, 7], [19, 3, 11], [19, 3, 13], [19, 3, 17], [19, 5, 2], [19, 5, 3], [19, 5, 5], [19, 5, 7], [19, 7, 2], [19, 7, 3], [19, 7, 5], [19, 7, 7], [19, 11, 2], [19, 11, 3], [19, 13, 2], [19, 13, 3], [19, 17, 2], [19, 17, 3], [19, 19, 2], [19, 23, 2], [23, 2, 2], [23, 2, 3], [23, 2, 5], [23, 2, 7], [23, 2, 11], [23, 2, 13], [23, 2, 17], [23, 2, 19], [23, 3, 2], [23, 3, 3], [23, 3, 5], [23, 3, 7], [23, 3, 11], [23, 3, 13], [23, 5, 2], [23, 5, 3], [23, 5, 5], [23, 5, 7], [23, 7, 2], [23, 7, 3], [23, 7, 5], [23, 11, 2], [23, 11, 3], [23, 13, 2], [23, 13, 3], [23, 17, 2], [23, 19, 2], [29, 2, 2], [29, 2, 3], [29, 2, 5], [29, 2, 7], [29, 2, 11], [29, 2, 13], [29, 2, 17], [29, 3, 2], [29, 3, 3], [29, 3, 5], [29, 3, 7], [29, 3, 11], [29, 5, 2], [29, 5, 3], [29, 5, 5], [29, 7, 2], [29, 7, 3], [29, 11, 2], [29, 11, 3], [29, 13, 2], [29, 17, 2], [31, 2, 2], [31, 2, 3], [31, 2, 5], [31, 2, 7], [31, 2, 11], [31, 2, 13], [31, 3, 2], [31, 3, 3], [31, 3, 5], [31, 3, 7], [31, 5, 2], [31, 5, 3], [31, 5, 5], [31, 7, 2], [31, 7, 3], [31, 11, 2], [31, 13, 2], [37, 2, 2], [37, 2, 3], [37, 2, 5], [37, 2, 7], [37, 2, 11], [37, 2, 13], [37, 3, 2], [37, 3, 3], [37, 3, 5], [37, 3, 7], [37, 5, 2], [37, 5, 3], [37, 5, 5], [37, 7, 2], [37, 7, 3], [37, 11, 2], [37, 13, 2], [41, 2, 2], [41, 2, 3], [41, 2, 5], [41, 2, 7], [41, 2, 11], [41, 3, 2], [41, 3, 3], [41, 3, 5], [41, 3, 7], [41, 5, 2], [41, 5, 3], [41, 7, 2], [41, 7, 3], [41, 11, 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Flowchart:

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