def list_prime_factors(number):
current = number
primes = []
factors = []
prime_generator = p003.primes(number+1)
def get_next_number(num):
if num in primes:
factors.append(num)
return num
for p in primes:
if num % p == 0:
factors.append(p)
num /= p
return get_next_number(num)
return num
while current not in primes:
try:
primes.append(prime_generator.next())
except StopIteration:
break
if current % primes[-1] == 0:
current = get_next_number(current)
assert(number == reduce(lambda x, y: x * y, factors))
return sorted(factors)
def get_nth_prime(n): prime_generator = primes() for i in xrange(n): prime = prime_generator.next() return prime
def first_n_to_n_prime_factors(n):
start_value = reduce(mul, islice(primes(),0,n))
factors = FactorList(10**(n+1))
for seq in izip(*[ count(start_value+i) for i in xrange(n) ]):
if all( len(set(factors.factor(num))) == n for num in seq ):
return seq
# Problem 7: https://projecteuler.net/problem=7
# By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13,
# we can see that the 6th prime is 13.
# What is the 10 001st prime number?
from p003 import primes
from math import log
n_th = 10001
def pi(x):
'''
Estimate the number os primes under x.
Source: https://primes.utm.edu/howmany.html
'''
return int(x/(log(x)-1))
N = 120000
print('Numbers os primes under {} is {}.'.format(N, pi(N)))
myprimes = primes(N)
print('The {} prime is {}.'.format(n_th, myprimes[n_th-1]))
def solve(): n = 10001 return next(islice(primes(), n-1, n))
# Problem 10: https://projecteuler.net/problem=10 # The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. # Find the sum of all the primes below two million. from p003 import primes myprimes = primes(2000000) print(sum(myprimes))
# Problem 5: https://projecteuler.net/problem=5
# 2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
# What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
from numpy import array, where, in1d
from p003 import primes
from functools import reduce
numbers = array(range(2,20+1))
myprimes = primes(20)
factors = []
for prime in myprimes:
had_division = True
while had_division:
remainders = numbers%prime
ix = in1d(remainders, 0)
had_division = ix.sum() > 0
if had_division:
factors.append(prime)
numbers[where(ix)] = numbers[where(ix)]/prime
print(reduce(lambda x,y: x*y, factors))