Prime Definition and 777 Threads

I Need someone to publish Grade 4 Prime Sequence Series Table, just add my name to it and were partners oh and teach this to your students, this took 40 years to develope https://www.youtube.com/watch?v=eDKK8pP1jiw

I am a Savant I count using Primes and Developed this Table Here ... Because I am a Math Savant I never had to go to University so I don't have any papers, I need a Student or Professor willing to Sign off on this Methodology of spotting Primes...Here is the Table with the Formulas all you...

https://imgur.com/a/9tDdMqt Hey So I am trying to prove this. I tried using linear combinations and not sure how that would help. I am just not familiar with combinatorics and wondering if anyone would enlighten me.

Hey! :o I am looking the follwong exercise: Using the method of Quine-McCluskey, determine the prime implicants for the following switching function and find a disjunctive minimal form. If available, also specify all other disjoint minimal forms. The switching function is...

Hey! :o I am looking at the following: Use the Quine-McCluskey method to determine the respective prime implicants for the following boolean functions and find a disjunctive minimal form. If available, also give all others disjunctive minimal forms. \begin{equation*}f(x_1, x_2, x_3...

Hello everyone! I was going through a simple high school level mathematics book and got to the following question: n2 - n + 41 is a prime for all positive integers n. You're supposed to find a counter-example and prove the statement false. You could of course sit and enter different...

Are all complex integers that have the same norm associates of each other? I have seen definitions saying that an associate of a complex number is a multiple of that number with a unit. And I understand that the conjugate of a complex number is also an associate. But I am looking for a...

Homework Statement Prove that if ##p## is a prime number and if ##p>5## then ##p^2-37## is divisible by ##12## Homework EquationsThe Attempt at a Solution So I think that the number ##p^2-37## should be expressed in a way that we can clearly see that it is divisible by 3 and by 2 twice...

This is no homework. I have come across a conjecture in a book called The art of the infinite:the pleasures of mathematics. I want to understand how to prove it. Homework Statement Consider a 3-rhythm starting with 2: ## 2, 5, 8, 11, 14, 17...## The each number in this sequenc has the form...

Homework Statement Let ##n## be odd and a composite number, prove that all of its prime is at most ##\frac{n}{3} ## Homework Equations Some theorems might help? Any ##n>1## must have a prime factor if n is composite then there is a prime ##p<√n## such that ##p|n## The Attempt at a Solution...

A couple days ago, a new Mersenne prime, $$2^{82589933}-1$$ has being found by GIMPS. It’s the number 51st Mersenne prime being found by men. Link to GIMPS’s website: https://www.mersenne.org/primes/?press=M82589933 Edit: According to my calculations using common logarithm, this number should...

I identified what appears to be a partitioning of all integers > 1 into mutually disjoint sets. Each set consists of an infinite series of integers that are all the powers of what I am calling a "root" r (r is an integer that has no integer roots of its own, meaning: there is no number x^n that...

Let $$g(n)$$ be the numerators of the elements of the recursion $$i(n)=i(n-1)+\frac{1}{i(n-1)}$$ when they are expressed in simplest form, with $$i(0)=1$$. Let $$p$$ be the smallest prime factor of $$g(m)$$. Show that $$p>4m-4$$.Homework Equations Euler's Theorem? The Attempt at a Solution OEIS...

I was reading an old thread about multiplying successive prime numbers adding 1 to obtain another prime number. I have worked with prime numbers for several years now and have developed what I best call a bi-linear advancement. It is an open-ended sieve of Eratosthenes. After many, many hours...

Hello! (Wave) I want to solve the following system of congruences: $$x \equiv 13 \pmod{40} \\ x\equiv 5 \pmod{44} \\ x \equiv 38 \pmod{275}.$$I have thought the following: $$x \equiv 13 \pmod{40} \Leftrightarrow x \equiv 13 \pmod{2^3 \cdot 5}$$ $$x \equiv 5 \pmod{44} \Leftrightarrow x \equiv...

Homework Statement Prove that if p is a prime number larger than 3, then ##p^2## = 6k + 1 for some k ∈ ℤ. Homework Equations * Modulo * Factoring * Distribution or ##(ax + b)^2 = a^2 x^2 + 2abx + b^2## formula The Attempt at a Solution The reason why p mod d = r_i, where r_i is the remainder...

I am reading The Basics of Abstract Algebra by Paul E. Bland ... I am focused on Section 7.2 Euclidean, Principal Ideal, Unique Factorization Domains ... ... I need help with the proof of Theorem 7.2.14 ... ... Theorem 7.2.14 and its proof reads as follows: In the above proof by Bland we...

If you have 2 integers n and n+1, it is easy to show that they have no shared prime factors. For example: the prime factors of 9 are (3,3), and the prime factors of 10 are (2,5). Now if we consider 9 and 10 as a pair, we can collect all their prime factors (2,3,3,5) and find the maximum, which...

I am reading The Basics of Abstract Algebra by Paul E. Bland ... I am focused on Section 3.2 Subrings, Ideals and Factor Rings ... ... I need help with the proof of Theorem 3.2.19 ... ... Theorem 3.2.19 and its proof reads as follows: In the above proof by Bland we read the following:"... ...

I am reading The Basics of Abstract Algebra by Paul E. Bland ... I am focused on Section 3.2 Subrings, Ideals and Factor Rings ... ... I need help with the proof of Theorem 3.2.16 ... ... Theorem 3.2.16 and its proof reads as follows: In the above proof of (3) \Longrightarrow (1) by Bland...

Hello everyone. [Firstly, I didn't know if this belongs here or in General; please move if appropriate]. <Moderator's note: moved to GD> I was reading this paper on the AKS primality test (undergraduates can understand it, highly recommended!), and on page 7 the author brings up the story of...

Using Wolfram I was able to make certain that the following number was a Prime: 123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901 However finding its position in Wolfram...

Homework Statement The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143 ? Homework EquationsThe Attempt at a Solution Here part of the my code #!/usr/bin/python import math N=99 for n in range (2,N): if N%n == 0...

1. The problem statement, all variables, and given/known data Create algorithm steps that for a given number (N) is prime or not Homework Equations 3. The Attempt at a Solution I am trying to create an algorithm but I am stuck at some place. Here is my trying. 1-Input a...

Homework Statement Consider ##F[x,y]##, where ##F## is some field. I've been working on a problem all day and I'm having trouble with this last step. I am trying to show that ##x \notin(x,y)^n## for any ##n \in \Bbb{N}##. Homework EquationsThe Attempt at a Solution Note that ##(x,y)^n =...

$M$ is the set of squares of the first $20$ natural numbers:\[M = \left\{1^2,2^2,3^2,...,19^2,20^2\right\}\]We say that $n$ is a good number, if in any subset of $M$ of size $n$ there are two elements $a$ and $b$ such that $a + b$ is a prime number. Find the smallest good number.

Regarding the recent discovery by Ken Ono and colleagues of the fractal structure of partition numbers for primes: a great lever of intuition would be to see a diagram, or any presentation of the numbers that reveals this fractal structure. Perhaps the fractal structure is somehow hidden in a...

Does there exist a polynomial P(x) with rational coefficients such that for every composite number x, P(x) takes an integer value and for every prime number x, P(x) does not take on an integer value? Can someone please guide me in the right direction? I've tried to consider the roots of the...

Hello! (Wave) We want to find an efficient algorithm that checks whether an odd number is a prime or not. In order to obtain such an algorithm, one tests the congruence $(X+a)^n \equiv X^n+a$ not "absolutely" in $\mathbb{Z}_n[X]$, but modulo a polynomial $X^r-1$, where $r$ have to be chosen in...

n^2 - 14n + 40, is this quadratic composite or prime - when n ≤ 0. Determine, all integer values of 'n' - for which n^2 - 14n + 40 is prime? Proof Required. ps. I can do the workings, but the 'proof' is the problem. Many Thanks John.

Homework Statement Let ##R## be a commutative ring with identity and suppose that ##A## is an ideal in ##R## contained in the finite union of prime ideals ##P_1 \cup \cdots \cup P_n##. Show that ##A \subseteq P_i## for some ##i##. Homework EquationsThe Attempt at a Solution The base case...

Homework Statement I don't understand the lemma. Homework EquationsThe Attempt at a Solution Isn't all prime number not a product of primes? The lemma doesn't make sense to me... Moreover, if m=2, m-1 is smaller than 2, the inequality also doesn't make sense. Please help me

Homework Statement Let ##f(x) = (x-a_1)...(x-a_n) \in k[x]##, where ##k## is a field. Show that ##f(x)## has no repeated roots (i.e., all the ai are distinct elements in ##k##) if and only if ##gcd(f,f')=1##, where ##f'(x)## is the derivative of ##f## Homework Equations ##(x-a)^2 |f(x)##...

Determine all prime numbers $p$ such that the total number of positive divisors of $A = p^2 + 1007$ (including $1$ and $A$) is less than $7$.

Hello! (Wave)Let $b_1< b_2< \dots< b_{\phi(m)}$ be the integers between $1$ and $m$ that are relatively prime to $m$ (including 1), and let $B=b_1 b_2 b_3 \cdots b_{\phi(m)}$ be their product. I want to show that either $B \equiv 1 \pmod{m}$ or $B \equiv -1 \pmod{m}$ . Also I want to find a...

Is there a set of $2015$ consecutive positive integers containing exactly $15$ prime numbers?

Homework Statement The book wants me to use direct proof. if p is a prime and k is an integer for which 0 < k < p, then p divides ##\left( \frac p k \right)## Homework Equations ##\left( \frac p k \right) = \frac {p!} {k!(p-k)!}## The Attempt at a Solution the fraction line in ##\left( \frac...

Homework Statement as listed above the question is how many and which three digit NIP can be formed whit the use of prime numbers[/B]Homework Equations nothing currently trying to understand[/B]The Attempt at a Solution well i have found at least 168 primer numbers below 1000 i mean in the...

I know that 2 is an even number. I equate prime numbers with odd numbers. Why is 2 a prime number when it is listed in a group of odd numbers? Is 2 the only, even prime number? Why?

What is the basic difference between an odd, composite and prime number? Give an example for each.

Hi, Can anyone please tell me any easy way of prime factorizing 5-digit composite numbers from 10,000 to 99,999 with little writing or mentally? Thanks.

A number can be factored into a product of its component factors A number can be factored into a product of its prime . But, What exactly is a prime number ? Prime numbers are numbers greater than 1 that are evenly divisible only by themselves and 1 Is it a number that can only be evenly...

45x2+15x +/-1. ... 59;61 ,209;211 ,449;451 ,779;781 ... 45x2- 15x +/-1 ... 29;31 ,149;151 ,359;361 ,659;661 ... Derived from 20x2-1 can only have factors ending in the digit _1, or _9 .

I am a commerce student But i decided to refresh my maths from some basics , i downloaded this book called algebra one for dummies . I have few doubts . What is the difference between Prime factors Greatest common factor (GCF) Least common multiple (LCM) Can i move to algebra factorization...

I am reading Abstract Algebra: Structures and Applications" by Stephen Lovett ... I am currently focused on Chapter 7: Field Extensions ... ... I need help with the proof of, or at least some remarks concerning, Proposition 7.1.3 ...Proposition 7.1.3 plus some introductory remarks (proof?)...

I am reading Abstract Algebra: Structures and Applications" by Stephen Lovett ... I am currently focused on Chapter 7: Field Extensions ... ... I need help with the proof of, or at least some remarks concerning, Proposition 7.1.3 ...Proposition 7.1.3 plus some introductory remarks (proof?)...

Is there a better way than guess and check?

Mod note: added code tags using System; using System.Collections.Generic; using System.Linq; using System.Text; namespace ConsoleApplication1 { class Program { static void Main(string[] args) { List<int> number = new List<int>(1000); // int list for 1000 numbers...

I believe this is probably a high level undergraduate question, but i could easily be underestimating it and it's actually quite a bit higher than that. I'm reading the Prime number theorem wikipedia page and I'm in part 4 under Proof sketch where sometime down they give in inequality: x is a...

I'm reading a book that mentions writing an algebraic expression in terms of its prime factors, for example: x2 - 2 x - 3 = (x + 1) (x - 3) I know what 'prime factors' means for a number but not for an expression. Aren't these just 'factors'?