buses.py

# I was sitting on a bus whose number's prime
# factorization was 37 x 113. The prime factorization of the
# number of the bus in front of me was 11 x 373. 
# I wonder how many other four-digit bus numbers 
# have a prime factorization with exactly those digits?

# pip install sympy 
from itertools import chain 
from sympy.ntheory import factorint

def strp(n,p):
    if p == 1:
        return str(n)
    return str(n) + "^" + str(p)

def strf(f):
    return "*".join([strp(k, f[k]) for k in sorted(f.keys())])

def f(x):
    fs = factorint(x)
    if sorted(list(chain(*[list(str(f)) for f in fs.keys()]))) == ['1', '1', '3', '3', '7']:
        if len(fs.keys()) == 2:
            print(x, strf(fs))

for x in range(1000,10000):
    f(x)

# 1781 13*137
# 2249 13*173
# 3707 11*337
# 4103 11*373
# 4121 13*317
# 4181 37*113
# 4247 31*137
# 4847 37*131
# 5321 17*313
# 5363 31*173
# 5627 17*331
# 8063 11*733
# 8249 73*113
# 9563 73*131
# 9827 31*317