## project euler problem #7

### Aside

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?

http://projecteuler.net/problem=7

highlight below for my solution:

```
#using a prime number set datastructure - https://gist.github.com/aausch/6709819
p =  PrimeSet()

i = 10001

while (len(p)<10001):
i in p
i += i

print sorted(list(p))```

`[More programming riddles]`

## project euler problem #5

### Aside

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?

http://projecteuler.net/problem=5

highlight below for my solution:

```
#using a prime number set datastructure - https://gist.github.com/aausch/6709819
p = PrimeSet()

def min_product(n):
n in p #initialize the PrimeSet with all primes less than n
product = 1
for prime in p:
product = product * (prime ** (int(n ** (1.0/prime))))
return product

print min_product(20)
```

`[More programming riddles]`

## project euler problem #3

### Aside

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

What is the largest prime factor of the number 600851475143 ?

http://projecteuler.net/problem=3

highlight below for my solution:

```
#using a prime number set datastructure - https://gist.github.com/aausch/6709819
p_set = PrimeSet()
n = 600851475143
sqrt = int(n ** 0.5)
p_set[sqrt]
max_factor = 1
for x in p_set:
if n % x == 0 and x > max_factor:
max_factor = x
print max_factor

```

`[More programming riddles]`