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Project Euler: Problem 3, Largest prime factor
The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number being input, input might be ui...

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Make a vector of prime numbers
Input(n) - length of vector with prime numbers Output(v) - vector of prime numbers Example: * n=1; v=2 * n=3; v=[2 3 5...

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Largest Twin Primes
<http://en.wikipedia.org/wiki/Twin_prime Twin primes> are primes p1, p2 = p1 + 2 such that both p1 and p2 are prime numbers. Giv...

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Sophie Germain prime
In number theory, a prime number p is a *Sophie Germain prime* if 2p + 1 is also prime. For example, 23 is a Sophie Germain prim...

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The Goldbach Conjecture
The Goldbach conjecture asserts that every even integer greater than 2 can be expressed as the sum of two primes. Given the eve...

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Multiples of a Number in a Given Range
Given an integer factor _f_ and a range defined by _xlow_ and _xhigh_ inclusive, return a vector of the multiples of _f_ that fa...

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Prime factor digits
Consider the following number system. Calculate the prime factorization for each number n, then represent the prime factors in a...

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Get all prime factors
List the prime factors for the input number, in decreasing order. List each factor. If the prime factor occurs twice, list it as...

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Factorize THIS, buddy
List the prime factors for the input number, in decreasing order. List each factor only once, even if the factorization includes...

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Triangle sequence
A sequence of triangles is constructed in the following way: 1) the first triangle is Pythagoras' 3-4-5 triangle 2) the second...

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Fibonacci-Sum of Squares
Given the Fibonacci sequence defined by the following recursive relation, * F(n) = F(n-1) + F(n-2) * where F(1) = 1 and F(1)...

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Project Euler: Problem 5, Smallest multiple
2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. What is the smalle...

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Project Euler: Problem 9, Pythagorean numbers
A Pythagorean triplet is a set of three natural numbers, a b c, for which, a^2 + b^2 = c^2 For example, 3^2 + 4^2 = 9 + 16 ...

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Project Euler: Problem 10, Sum of Primes
The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. Find the sum of all the primes below the input, N. Thank you <http:/...

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Project Euler: Problem 6, Natural numbers, squares and sums.
The sum of the squares of the first ten natural numbers is, 1^2 + 2^2 + ... + 10^2 = 385 The square of the sum of the first ...

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Project Euler: Problem 1, Multiples of 3 and 5
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...

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Television Screen Dimensions
Given a width to height ratio of a TV screen given as _w_ and _h_ as well as the diagonal length of the television _l_, return t...

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Calculate the area of a triangle between three points
Calculate the area of a triangle between three points: P1(X1,Y1) P2(X2,Y2) P3(X3,Y3) these three points are the vertices of ...

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Right Triangle Side Lengths (Inspired by Project Euler Problem 39)
If p is the perimeter of a right angle triangle with integral length sides, { a, b, c }, there are exactly three solutions for p...

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Are all the three given point in the same line?
In this problem the input is the coordinate of the three points in a XY plane? P1(X1,Y1) P2(X2,Y2) P3(X3,Y3) how can...

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Volume of a Parallelepiped
Calculate the volume of a Parallelepiped given the vectors for three edges that meet at one vertex. A cube is a special case ...

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Angle between Two Vectors
The dot product relationship, a dot b = | a | | b | cos(theta), can be used to determine the acute angle between vector a and ve...

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Is the Point in a Circle?
Check whether a point or multiple points is/are in a circle centered at point (x0, y0) with radius r. Points = [x, y]; c...

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What is the distance from point P(x,y) to the line Ax + By + C = 0?
Given a point, P(x,y), find the distance from this point to a linear line. INPUTS: x, y, A, B, C OUTPUTS: d, the distance ...

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Angle between two vectors
You have two vectors , determine the angle between these two vectors For example: u = [0 0 1]; v = [1 0 0]; The a...

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Similar Triangles - find the height of the tree
Given the height, h1, of a power pole, shorter than a tree, a given distance, x2 away, please find h2, height of the tree. Pleas...

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Circumscribed circles
Given the lengths of the 3 sides of a triangle, output the radius of the circumscribed circle. Example: [3 4 5] -> 2.5

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Are you in or are you out?
Given vertices specified by the vectors xv and yv, and a single point specified by the numbers X and Y, return "true" if the poi...

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Smallest distance between a point and a rectangle
Given two points *x* and *y* placed at opposite corners of a rectangle, find the minimal euclidean distance between another poin...

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Great Circle Distance
Find shortest between two points on a ball given their azimuthal and polar angles (in degrees) as well as the radius of the sphe...

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