def prop(expansion):
na = digitNumber(expansion.a)
nb = digitNumber(expansion.b)
if na > nb:
return True
return False
def test_property(pr_set, n):
global pc
if not pc.prime(n):
return False
log_n = digitNumber(n)
for a in pr_set:
log_a = digitNumber(a)
if not pc.prime(a*(10**log_n) + n):
return False
if not pc.prime(n*(10**log_a) + a):
return False
return True
# The 5-digit number, 16807=7^5, is also a fifth power. Similarly, the 9-digit
# number, 134217728=10^9, is a ninth power.
# How many n-digit positive integers exist which are also an nth power?
from utils import digitNumber
from time import time
startTime = time()
total = 0
lim = 100
for n in range(1, lim):
for m in range(1, lim):
tmp = digitNumber(m ** n)
if tmp == n:
print(m ** n, n)
total += 1
elif tmp > n:
break
print(total)
print(time() - startTime)