I was messing around with a homebrew (and offbeat) factoring method which popped up a couple of factors for 2^2049-1. I've checked factoredM.txt and they...
... In http://www.garlic.com/~wedgingt/factoredM.txt at M( 683 ) (683 divides 2049). ... In lowM.txt at M( 2049 ). My lowM.txt is from February 2005 but I...
I'm wondering how my current factoring program compares to other methods used in terms of the amount of work needed to find the factors. Factored here are...
... If you really wondered how it compares to other methods, why have you not compared it to other methods? Grab Miracl, and see how quickly P-1, P+1, Rho, and...
I want to make a conjecture that no definition of primes can include 2 to be a prime. A definition based on addition is the following and excludes 2 to be a...
... A good warning, Paul. In case this reference is confusing to some, here's an explanation. This is from an article by Kurt Salzinger of the American...
Simon, I like your comments. Indeed, the primes may represent a code for the ETI or even the supernatural God to communicate with humans. But mere awareness...
Hello all, That last discussion got me to thinking about something I use as a visualization to understand primes and their distribution. I'd like to share it...
On Behalf Of shuangtheman ... The objective truth is simple and obvious (for integers): 2 is prime. Those that can not understand such a trivial definition...
... Then you are at odds with the Fundamental Theorem of Arithmetic. Also, there is a very basic way to define prime -- perhaps the most basic way of all....
... Come up with your own definition of a term that already has a well-established unwavering definition. Don't do that, m'kay? ... The Tietze citation looks...
I actually think division by zero is not defined. I suggest the definition of primes using set theory: A prime is a natural number, whichs set of divisors has...
... I would suggest that one can define divisibility by zero without needing a definition for division by zero. Say that X is divisible by A if there exists...
I want this following commentary to be given some thought, instead of scorn. Here are two conjectures: a} Every even number equal to or greater than 6 is the...
... Why do you discount the possibility of thought and then scorn? ... Nonsense. They are not proven yet because thus-far-performed mathematically-sound...
Sorry, but I do not agree. Due to correction: a) I think divisibility is defined for natural numbers only. b) You suggested "Say that X is divisible by A if...
... With what? Please don't top-post, m'kay? ... But Jack provides a definition which works for N \/ { 0 }. Yes, there exist a handful of simple and convenient...
it is known that there exist real positive numbers theta such that the integer part of theta^3^n is a prime number, for all positive integers n. The least such...
... It depends on the area people work in. For a combinatorian, the equality 0^0 = 1 can work perfectly well; as the left-hand-side denotes the number of...
Questions: (1) If 2 and 5 are both cubic residues of a prime p, is 10 a cubic residue please? (2) Does the same apply to quatic and highr order residues? (3)...
... If A is a cubic residue, that means there is an a such that a^3 = A. So yes, if A and B are cubic residues (say the cubes of a and b), so is their product...
So I thank everybody very much for explanation. Mathematics has more hidden beauties I will ever learn, and as I am not in a professional way dealing with...
1. A prime is a positive integer that cannot be expressed by the even number of sums of any single number except 1 and itself. 2. A prime is a positive...
... I already did, but let me rephrase it in a more concise way... *************************************************************** A natural number X is prime...
I can also give you a definition that will include 2 as a prime: A prime is a positive integer that has only two divisors, regardless whether it has smaller...
Following a list of primes that starts with 2, the author Derbyshire wrote: “At this point, someone usually objects that 1 is not included in this or any ...
