예제 #1
0
def cycle(i):
    factors = prime_factors(i)
    # Filter out all 2s and 5s

    i = 1
    for p in factors:
        if p != 2 and p != 5:
            i = i * p

    if i == 1:
        return 0

    digits = 1
    n = 9
    while n % i != 0:
        n = n * 10 + 9
        digits = digits + 1
    return digits
예제 #2
0
#!/usr/bin/env python3
'''
Largest prime factor

The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143 ?
'''

from sys import argv

from prime import prime_factors

if __name__ == '__main__':
    try:
        target = int(argv[1])
    except IndexError:
        target = 600851475143
    print(max(prime_factors(target)))
예제 #3
0
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 collections import defaultdict
from sys import argv

from prime import prime_factors


if __name__ == "__main__":
    try:
        target = int(argv[1])
    except IndexError:
        target = 20

    powers = defaultdict(int)

    for n in range(2, target + 1):
        prime_powers = prime_factors(n)
        for k in prime_powers:
            powers[k] = max(powers[k], prime_powers[k])

    total = 1
    for k in powers:
        total *= k ** powers[k]
    print(total)
예제 #4
0
def num_divisors(x):
    # Based on http://mathschallenge.net/index.php?section=faq&ref=number/number_of_divisors
    factors = prime_factors(x)
    return reduce(lambda x, y: x * (y + 1), factors.values(), 1)
예제 #5
0
파일: 015.py 프로젝트: yulvil/euler-python
import prime

def com(n,k):
    return factorial(n)/(factorial(n-k)*factorial(k))

def com(n,k):
    return factorial(n)/(factorial(n-k)*factorial(k))

b = (0,0)
e = (2,2)

p = [(0,1),(0,1),(1,0),(1,0)]
r = set([pp for pp in permutations(p)])
#print(r)
print(len(r))

# Too big
#p = [(0,1),(0,1),(0,1),(0,1),(0,1),(0,1),(0,1),(0,1),(0,1),(0,1),(1,0),(1,0),(1,0),(1,0),(1,0),(1,0),(1,0),(1,0),(1,0),(1,0)]
#r = set([pp for pp in permutations(p)])
#print(r)
#print(len(r))

print( com(52,5) )
print( com(500,5) )
res = com(2,1)*com(10,1)*com(2,1)*com(10,1)*com(2,1)*com(9,1)*com(2,1)*com(9,1)*com(2,1)*com(8,1)*com(2,1)*com(8,1)*com(2,1)*com(7,1)*com(2,1)*com(7,1)*com(2,1)*com(6,1)*com(2,1)*com(6,1)*com(2,1)*com(5,1)*com(2,1)*com(5,1)*com(2,1)*com(4,1)*com(2,1)*com(4,1)*com(2,1)*com(3,1)*com(2,1)*com(3,1)*com(2,1)*com(2,1)*com(2,1)*com(2,1)
print( res )

print( prime.prime_factors(res / 137846528820) )
print( prime.prime_factors(137846528820) )

# unsolved
예제 #6
0
The first two consecutive numbers to have two distinct prime factors are:

    14 = 2 × 7
    15 = 3 × 5

The first three consecutive numbers to have three distinct prime factors are:

    644 = 2² × 7 × 23
    645 = 3 × 5 × 43
    646 = 2 × 17 × 19.

Find the first four consecutive integers to have four distinct prime factors.
What is the first of these numbers?
'''

from itertools import count

from prime import prime_factors

if __name__ == '__main__':
    sequence = 0
    for number in count(1):
        if len(prime_factors(number)) == 4:
            sequence += 1
            if sequence == 4:
                print(number - 3)
                break
        else:
            sequence = 0
예제 #7
0
from prime import get_primes, prime_factors

max_prime = 300000

primes = get_primes(max_prime)

i = 0
while i < max_prime-3:
    if len(prime_factors(i+3, primes)) == 4:
        if len(prime_factors(i+2, primes)) == 4:
            if len(prime_factors(i+1, primes)) == 4:
                if len(prime_factors(i, primes)) == 4:
                    print(i)
                else:
                    i += 1
            else:
                i += 2
        else:
            i += 3
    else:
        i += 4

예제 #8
0
    Each tuple is create by taking a digit from :param digits: and removing the first instance of that digit from both i and j. If this would cause either i or j to be 0, then that tuple is skipped.
    """
    return filter(
        lambda x: x[0] > 0 and x[1] > 0,
        ((int(str(i).replace(d, '', 1)), int(str(j).replace(d, '', 1)))
         for d in digits))


fract = [1, 1]
for i in range(10, 100):
    i_digits = set(str(i))

    for j in range(i + 1, 100):
        if i % 10 == 0 and j % 10 == 0:
            continue

        j_digits = set(str(j))
        inter = i_digits.intersection(j_digits)

        for n, d in generate_test_fractions(i, j, inter):
            if isclose(i / j, n / d):
                print("{}/{} == {}/{}".format(i, j, n, d))
                fract[0] *= n
                fract[1] *= d

fract = cancel_common_factors(prime_factors(fract[0]), prime_factors(fract[1]))

print("Denominator of products: {}".format(expand_factorization(fract[1])))
print("Execution time: {}".format(time.time() - start_time))
예제 #9
0
divisibility_target = 500


def merge_factors(factorization_1, factorization_2):
    """Requires parameters in format returned by prime.prime_factors."""
    factors = set(factorization_1).union(factorization_2)
    return {
        k: factorization_1.get(k, 0) + factorization_2.get(k, 0)
        for k in factors
    }


# the first constiuent of the closed form of a triangle number: n(n+1)/2
n = 1
n_factors = dict()
next_factors = prime_factors(n + 1)

factor_count = 1

while factor_count <= divisibility_target:
    n += 1
    n_factors = next_factors
    next_factors = prime_factors(n + 1)

    merged = merge_factors(n_factors, next_factors)

    # There will always be an extra factor of 2 (see closed form), which is divided out
    merged[2] -= 1

    # The actual number of factors (prime and otherwise) is given by this product
    factor_count = reduce(mul, (v + 1 for v in merged.values()))
예제 #10
0
from prime import prime_factors

distinct_primes = [1, 1, 1, 1]

n = 647

still_checking = True

while still_checking:
    distinct_primes[0] = distinct_primes[1]
    distinct_primes[1] = distinct_primes[2]
    distinct_primes[2] = distinct_primes[3]
    s = set(prime_factors(n))
    distinct_primes[3] = len(s)
    if distinct_primes[0] > 3 and distinct_primes[1] > 3 and distinct_primes[2] > 3 and distinct_primes[3] > 3:
        still_checking = False
        print(n)
    else:
        n += 1

예제 #11
0
파일: 003.py 프로젝트: yulvil/euler-python
#/bin/python

# http://projecteuler.net/problem=3

# The prime factors of 13195 are 5, 7, 13 and 29.  What is the largest prime factor of the number 600851475143?

import prime

fact = prime.prime_factors(600851475143)
print( fact )       # [71, 839, 1471, 6857]
print( max(fact) )  # 6857
예제 #12
0
def main():
    print(max(prime_factors(600851475143)))
예제 #13
0
import prime

print(prime.prime_factors(600851475143))
예제 #14
0
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 collections import defaultdict
from sys import argv

from prime import prime_factors


if __name__ == '__main__':
    try:
        target = int(argv[1])
    except IndexError:
        target = 20

    powers = defaultdict(int)

    for n in range(2, target + 1):
        prime_powers = prime_factors(n)
        for k in prime_powers:
            powers[k] = max(powers[k], prime_powers[k])

    total = 1
    for k in powers:
        total *= k ** powers[k]
    print(total)