Euler 007

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 10001st prime number?

My solution below.

Euler 006

Next!

The sum of the squares of the first ten natural numbers is,
1² + 2² + ... + 10² = 385
The square of the sum of the first ten natural numbers is,
(1 + 2 + ... + 10)² = 55² = 3025
Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 - 385 = 2640.
Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

Didn't brute force this one. Read about math instead: 

Summation

Square Pyramidal Numbers

Going to move the solutions inside the fold.

Euler 005

Sorry for three in one day, but this one was awesome in Haskell.

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?

Neil, you might punch me for this one.

Euler 004

Problem 004: 

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 X 99.
Find the largest palindrome made from the product of two 3-digit numbers.

BOOM:

Euler 003

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

My response:

Euler 002

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...

By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.

My solution, in Haskell:

Euler 001

The first Project Euler problem asks

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below 1000.

Here's my solution, implemented in Haskell: