def get_n_digit_primes(n):
prime_list = []
for i in prime_sieve(10**n):
if num_digits(i) == n:
prime_list.append(i)
return prime_list
def p063(n):
lower_bound = ceil(10**((n-1)/n))
i = lower_bound
num = i**n
count = 0
while num_digits(num) == n:
print(i, num)
i += 1
count += 1
num = i**n
return count
from euler import num_digits
from time import time
T = time()
# add a number num to the fraction frac
# return the new fraction
def add_num_frac(num, frac):
return [num*frac[1] + frac[0], frac[1]]
def rev_frac(frac):
return frac[::-1]
def P057(iter):
result = rev_frac(add_num_frac(2, [1, 2]))
for i in range(0, iter-2):
result = rev_frac(add_num_frac(2, result))
result = add_num_frac(1, result)
return result
limit = 1000
count = 0
for i in range(1, limit+1):
f = P057(i)
if num_digits(f[0]) > num_digits(f[1]):
count += 1
print(count)
print("time elapsed ", time() - T)
# https://projecteuler.net/problem=97
from euler import num_digits
from time import time
T = time()
s = 28433
for i in range(0, 7830457):
s *= 2
if num_digits(s) == 11:
s %= (10**10)
print(s + 1)
print('Time elapsed:', time() - T)
# notice that python can do it easily (and faster) just by inputting the formula
# print((28433 * (2 ** 7830457) + 1) % (10**10))
