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Primes of the form x^2 + ny^2 David A. Cox
Publisher: Wiley-Interscience

Cox Publisher: Wiley-Interscience. N+1 prime problem Are there an infinite number of primes of the form x2+1. CON: The notion of a coloring of the plane (or even a piece of paper which is what I would use) is somewhat abstract. It is known that no matter how you two-color the first nine numbers 1,2, … ,9, you will always have a monochromatic set of 3 evenly spaced integers. There are twelve possible ways of making figure eights: The Twelve Solutions include (The first two numbers are the top segment $AB$, the second two numbers form the bottom segment $CD$.): 1-2-9-3 2-4-1-5 By viewing a list of primes, you' ll find exactly 7 pairs of primes with the desired property: $$\left\{(2,5), (3,7), (5,11), (11,23), (23,47), (29,59), (41,83)\right\}$$. Cooper's find is part of the Great Internet Mersenne Prime Search (GIMPS) —a distributed computing project that hunts down Mersenne primes. Primes of the form x^2 + ny^2 David A. Fall 2012 Problem Set 4 Each step changes the $x$ or $y$ coordinate by 1. In other words, they form a three-term arithmetic progression. Download Primes of the form x^2 + ny^2. Provides a general solution to the question of which primes p can be expressed in the form x² + ny². In addition, the number is the 48th example of a rare class of primes called Mersenne Primes. Mersenne primes take the form of 2 raised to the power of a prime number minus 1. Primes of the form x^2 + ny^2 by David A.