In [1]:
import sympy as sym
import numpy as np
import math

from IPython.display import display, Math
from sympy.abc import w,x,y,z,a,b,c,d
sym.init_printing()
In [2]:
number = 48

fact_dict = sym.factorint(number)

fact_dict
Out[2]:
$$\left \{ 2 : 4, \quad 3 : 1\right \}$$
In [3]:
type(fact_dict)
Out[3]:
dict
In [4]:
list(fact_dict.keys())
Out[4]:
$$\left [ 2, \quad 3\right ]$$
In [5]:
nums = range(2,51)

for numi in nums:
    di = sym.factorint(numi)
    ks = list(di.keys())
    #print(ks)
    
    if len(di)==1 and di[ks[0]]==1:
        print('%g is a prime number' %numi)
    else:
        print('%g is a composite number with prime factors: %s' %(numi, list(di.keys())))

2 is a prime number
3 is a prime number
4 is a composite number with prime factors: [2]
5 is a prime number
6 is a composite number with prime factors: [2, 3]
7 is a prime number
8 is a composite number with prime factors: [2]
9 is a composite number with prime factors: [3]
10 is a composite number with prime factors: [2, 5]
11 is a prime number
12 is a composite number with prime factors: [2, 3]
13 is a prime number
14 is a composite number with prime factors: [2, 7]
15 is a composite number with prime factors: [3, 5]
16 is a composite number with prime factors: [2]
17 is a prime number
18 is a composite number with prime factors: [2, 3]
19 is a prime number
20 is a composite number with prime factors: [2, 5]
21 is a composite number with prime factors: [3, 7]
22 is a composite number with prime factors: [2, 11]
23 is a prime number
24 is a composite number with prime factors: [2, 3]
25 is a composite number with prime factors: [5]
26 is a composite number with prime factors: [2, 13]
27 is a composite number with prime factors: [3]
28 is a composite number with prime factors: [2, 7]
29 is a prime number
30 is a composite number with prime factors: [2, 3, 5]
31 is a prime number
32 is a composite number with prime factors: [2]
33 is a composite number with prime factors: [3, 11]
34 is a composite number with prime factors: [2, 17]
35 is a composite number with prime factors: [5, 7]
36 is a composite number with prime factors: [2, 3]
37 is a prime number
38 is a composite number with prime factors: [2, 19]
39 is a composite number with prime factors: [3, 13]
40 is a composite number with prime factors: [2, 5]
41 is a prime number
42 is a composite number with prime factors: [2, 3, 7]
43 is a prime number
44 is a composite number with prime factors: [2, 11]
45 is a composite number with prime factors: [3, 5]
46 is a composite number with prime factors: [2, 23]
47 is a prime number
48 is a composite number with prime factors: [2, 3]
49 is a composite number with prime factors: [7]
50 is a composite number with prime factors: [2, 5]