... [...] ... pn is the largest prime. ... You are right when you say W+1 is not in the set, but are wrong when you say it has to be prime. You are missing one...
Hi, I have been investigating some old buddies in the realm of prime numbers. If we take for example the first 999 digits of Pi and append that to the...
... From the prime page An arithmetic sequence (or arithmetic progression) is a sequence (finite or infinite list) of real numbers for which each term is the...
I make my case even easier. Keep in mind I am not talking about prime progressions. Every odd number not divisible by 3 can be expressed in distinctly one of ...
I was wondering if the schools were still teaching the old, out-dated system of dividing every odd number to test for primality. Everyone is so interested in...
How do I solve this equation. Find a and b for a given prime p. What properties must p have for a solution to this equation to exist. a^2 + b^2 = 0 (mod p) and...
... Not much interesting about this. Since a^2 = -b^2 (mod p), we have that solutions exist iff -1 is a quadratic residue mod p. If it is, let i denote a...
... This problem is not very well posed. Solutions to that equation exist for /any/ prime p, as all it says is that p divides the lhs! I think you want the...
... Well I see your point, the proof of FLT is a little complex for most people. But that point of view could also be said to de-value the achievments of some...
I don't like being told "never",but I have played with primes off and on for years and found no pattern to them. I have recently discovered that there is a...
Hi Euler (1772) x^2-x+41 is prime for x from 0 to 40 Legendre (1798) x^2+x+41 is prime for x from 0 to 39 Chaffey (2003) 2x^2-88x+997 is prime for x from 0 to...
http://www.primepuzzles.net/problems/prob_037.htm :) I'm currently working on the same idea and over the last year i've found out several simple properties of...
... It is as easy to de-value as it is to criticize. ... Does this mean you now agree that the infinitude of primes can be demonstrated by Dirlichlet's ...
... Dirichlet's theorem proves that there are an infinite number of primes in certain infinite subsets of the integers. So the fact that the total number of...
I would like to call primes of the form a^2+b^2=prime, pythagorean primes. Can anyone proove that there are infinite pythagorean primes? How about the...
... Or you could just call them Gaussian primes, which is more or less what they are. You should be able to find necessary information in any introductory...
If both a and b are nonzero then z=a+bi, is a Gaussian prime iff a^2+b^2 is an ordinary prime. So there is actually no name for primes of the form a^2+b^2 ...
... "Every prime of the form 4n+1 is the sum of two squares. Euler first communicated the following elegant proof of this fact to Goldbach in 1749, two years...
Elevensmooth, http://www.math.uchicago.edu/~kobotis/media/163/kim.pdf prooves there are infinite primes of the from a^2+b^2 So what about when b=a+1 Any...
... Then it becomes a univariate quadratic polynomial with interger coefficients. No univariate polynomial of degree greater than has ever been proved to...
I am not sure if this series has finite number of primes or not. I think it has infinite primes. I have found several primes in the 10000 digit category. I...
... But that is a question you will never be able to answer, one way or another, if all you're doing is search for primes of this type using computer methods....
Here is my proof for infiniteness of these primes if b=a+1 then we get 2*a^2+2*a+1 =p solving this a is an integer if there is a prime p such that 2*p-1=m^2 or...
Yes. Liu's prime formula is the first formula, which can prove further properties of primes. I wish that you may use the idea to get great success. I try prove...
An information type model of the primes applied to odd numbers: Odd Numbers---------> Primes ^ I Info function for Primes as Shannon Noise power function based...
Hey guys! I've recently done some more work on so-called "Wilde Primes" although I suggest that if we keep any of Jon Perry's name we should call them "Perry...
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