# primes

1. ### Showing a Prime exists

Professor decided to give more "optional" homework. Let A = {4k +1 | k ∈ Z^+ }. Show that there exists a prime p of A, and elements j, k, of A, such that p | (jk), but p does not divide j or k. In words: "Let A equal the set of elements of 4k+1, where k is an element of all positive integers...
2. ### Find the primes in Q[√−1] which have norm less than 6...

[SOLVED] Find the primes in Q[√−1] which have norm less than 6... Find the primes in Q[√−1] which have norm less than 6. Do the same for the primes inQ[√−3], and the primes in Q[√−5]. Group them according to which ones are associates of each other. Prove that the numbers you list are, indeed...
3. ### A Series of Questions About Some Series: Primes, Waves, and Factors

A Series of Questions About Some Series: Primes, Waves, and Factors Abstract A Trigonometric Series is crafted that gives the number of factors of x for all x. It is then manipulated to list all those factors. It is then used to give the exact distribution of the primes. It is then changed...
4. ### A method to show there are infintely many Twin Primes

This is an attempt at a Twin Prime Conjecture Proof, and is open to Peer Review. Abstract: Surfaces representing the primes and composites, the upper twin prime, the difference between squares, and the relations among them, are used to select input for a quadratic in such a way as to always...
5. ### My proof about primes MUST be invalid, but I don't know why

Short version: as stated in the title, I know the proof MUST be wrong, and I'd be very grateful if someone could point out the flaw(s) in my logic. https://goo.gl/osZr60 it's about 5 pages long, but not dense at all, so it should be a light and rather fast reading. Thanks in advance. Longer...
6. ### If p and q are primes then every group of order p^m q^n is solvable.

Hi: Burnside proved (using representation theory) that the number of elements in a conjugacy class of a finite simple group can never be a prime power larger than 1. Use this fact to prove Burnside's theorem: If p and q are primes then every group of order p^m q^n is solvable. What I did: let...
7. ### Proof by Induction - Primes and Euclid's Lemma

Hi guys, I'm having some trouble with this proof. Here's the question: Use mathematical induction and Euclid's Lemma to prove that for all positive integers s, if p and q1,q2,...,qs are prime numbers and p divides q1q2...qs, then p=qi for some i with 1 ≤ i ≤ s. Here's what I know: Euclid's...
8. ### Using Waves to determine Primes, Composites, Number's Factors, and their Distribution

Using Waves to determine Primes, Composites, Number's Factors, and their Distributions. William R. Blickos Introduction: This paper provides a method using periodic functions to check for primality, count factors, list factors, calculate the prime distribution, and determine the Nth prime...
9. ### Find all primes that satisfy the condition

$p|2^p+1$ p is a prime I know how to prove this but I need some help in steps. In factoring $2^p+1$ we will always have a term (2+1) because we know that $a^n + b^n = (a+b)\cdot P$ where P is a polynomial... I know this is true but I don't know how to prove it But if i can prove the thing...
10. ### proof involving primes.

Show that only one prime can be expressed as n^3 -1 for some natural numbers. I know that. (2)^3 - 1 = 7 but don't know how to show the proof, please help.
11. ### Emergence Of Twin Primes II

The goal of this paper is to introduce the concept of „Potential Primes“ within a given set of natural numbers, the maximum of which will be calculated as the product of the first n consecutive Prime Numbers. This concept will be used to demonstrate a mechanism for the emergence of Twin Primes...
12. ### Emergence Of Twin Primes

The goal of this paper is to introduce the concept of „Potential Primes“ within a given set of natural numbers, the maximum of which will be calculated as the product of the first n consecutive Prime Numbers. This concept will be used to demonstrate a mechanism for the emergence of Twin Primes...
13. ### Quadratic Residues of Primes

Use induction to show that, for all n, there exists a set of n distinct odd primes {p1,...,pn} such that every prime in the list is a quadratic residue modulo anyother prime in the list. I'm confused as to how we can construct the pk+1 prime such that it is a quadratic residue for {p1,...,pn}...
14. ### Sets of Primes

We have this set of primes which is infinite. This has lots of different subsets. Here is the list of subsets: Real Eisenstein primes: 3x + 2 Pythagorean primes: 4x + 1 Real Gaussian primes: 4x + 3 Landau primes: x^2 + 1 Central polygonal primes: x^2 - x + 1 Centered triangular primes: 1/2(3x^2...
15. ### Hi Very interested in primes

Hi guys. I have been to forums on math but not this particular one. I am very interested in primes and in fact I have a link to a page that has all kinds of primes. Here it is: https://oeis.org/wiki/User:Charles_R_Greathouse_IV/Tables_of_special_primes
16. ### primes squared inf showing a pattern with the last digits

1. so if i take a prime and square, cube, etc inf times, the last numbers will (so far) be four numbers repeating inf. 2. if i take 5 to the 3rd power and up inf times the last 3 numbers will alternate between 125 and 625. My background in this is type of working numbers is non existent. Up...
17. ### Pairs of primes and Cardinalities of sets

For a pair of primes (p_0,p_1), let Condition A be the following: For all integers n>0, \mbox{card}\left( \left\{ p_{1-j}^i \in \mathbb{Z} / p_j^n \mathbb{Z} \mid i \in \mathbb{N} \right\} \right) = p_j^n-p_j^{n-1} for both j=0 and j=1. Let M be the set of all pairs of primes that satisfy...
18. ### Pairwise distinct primes

Let n = p1.....pm for pairwise distinct primes pi other than 2 and 5. Let ki be the period of the decimal expression of 1/pi. Show that the period of the decimal expression of 1/n is the least common multiple of k1,....,km.
19. ### Euclid's proof of infinitude of primes...

Hi, I'm new into the domain of proofs, and I'm reading How to prove it - A structured approach. I'm having a problem with the last paragraph... If m is a product of primes, and q is one of those primes taken randomly, then we should be able to divide m by q to obtain the rest of the...
20. ### Hi MHF here's my conjecture on cycle length and primes : prime abc conjecture PAC

My nickname is miket and have many other nickname, research on natural science.I am interested in number theory.I put forward a conjecture on cycle length and primes : prime abc conjecture PAC. prime abc conjecture PAC: Suppose a>9 is odd and b is the cycle length of a as defined below. Then I...