def solve():
"""
>>> solve()
428570
"""
best = 2 / 5, 2, 5
primer = CachedPrimer()
for denominator in range(2, 1000001):
if denominator % 1000 == 0:
print(denominator)
denominator_prime_factors = primer.prime_factors(denominator).keys()
numerator = best_numerator_using_binary(denominator)
assert numerator / denominator < TARGET
def hcf_is_1(numerator):
common_factors = (primer.prime_factors(numerator).keys()
& denominator_prime_factors)
return not common_factors
while numerator / denominator > best[0] and not hcf_is_1(numerator):
numerator -= 1
current = numerator / denominator
assert current < TARGET
if current > best[0]:
best = current, numerator, denominator
# Ended up using the code from both wrong solutions. Cool!
return best[1] # (0.42857128571385716, 428570, 999997)
def solve():
"""
>>> solve()
142913828922
"""
primer = CachedPrimer()
known_primes = primer.primes_up_to(2000000)
return sum(known_primes)
def solve():
"""
>>> solve()
104743
"""
primer = CachedPrimer()
primes = primer.primes_up_to(stop_at_n_primes=10001)
return primes[-1]
def solve():
"""
>>> solve()
232792560
"""
PRIMER = CachedPrimer()
factors = collections.Counter()
for i in range(1, 21):
for factor, power in PRIMER.prime_factors(i).items():
factors[factor] = max(power, factors[factor])
return math.prod(factor**power for factor, power in factors.items())
def solve():
"""
>>> solve()
76576500
"""
primer = CachedPrimer()
number = 1
print(
candidates,
smallest_possible_500_factors,
primer.factors_count(smallest_possible_500_factors),
)
index = 1
best_count = 0
while (count := primer.factors_count(number)) <= 500:
index += 1
number += index
if count >= best_count:
best_count = count
print(number, best_count)
import collections import itertools import math import wrapt_timeout_decorator from common.primer import CachedPrimer PRIMER = CachedPrimer() # def smallest_possible_500_factors(): # INCORRECT # first_500_primes = PRIMER.primes_up_to(stop_at_n_primes=500) # best = math.inf # prime_count = 500 # while prime_count > 1: # factors = itertools.chain(*zip(*(first_500_primes for _ in range(prime_count)))) # candidate = 1 # used_factors = collections.Counter() # while math.prod(used_factors.values()) < 500: # factor = next(factors) # used_factors[factor] += 1 # candidate *= factor # if prime_count == 4: # print(factor) # prime_count -= 1 # best = min(candidate, best) # return best
from common.primer import CachedPrimer
def sum_digits(n):
return sum(int(char) for char in str(n))
PRIMER = CachedPrimer()
generators = []
for n in range(1, 100000001):
last_digit = n % 10
# if n > 6 and not last_digit in {2, 8, 0}:
# continue
if all(
PRIMER.is_prime(factor + n // factor)
for factor in PRIMER.factors(n)):
generators.append(n)
print(n, last_digit in {2, 8, 0}, PRIMER.prime_factors(n))