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Questions tagged [prime-numbers]

Prime numbers are natural numbers greater than 1 not divisible by any smaller number other than 1. This tag is intended for questions about, related to, or involving prime numbers.

A prime number (or a prime) is an element of the greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number ... The fundamental theorem of arithmetic establishes the central role of primes in :

Any integer greater than 1 can be expressed as a product of primes that is unique up to ordering.

Here you get the first 50 millions of primes.

The concept of prime numbers is extended in ring theory, where an element $p$ of a ring $R$ is prime if and only if whenever $p\mid ab$, then $p\mid a$ or $p\mid b$.

One can easily see that this extends the definition of prime numbers in the natural numbers.

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Group Theory. I worked on it . but ı couldn't reach any clear proof

If G is a group of order p^n and N is a normal subgroup of order p where p is prime and n is natural number, then prove that N is contained in the center of G.
Richard
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prove that $n >2$ and $n$ is a prime then $n$ is odd

$n > 2$ and $n$ is a prime number then $n$ is odd. Prove by contradiction assume $n$ is even then there is some $k\in\Bbb N, n = 2k$ then $n >2, 2k > 2 , k > 1$ Is this a sufficient proof?
user105696
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Co-prime power modulo

Is there $p$ such that $a^p\,$mod$\,r=0$ and $r$ is a prime number and $1\le a
hanugm
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check for a number is divisible or not

I have a very very large integer (but it's form is specific), how can i test if this integer is divisible or not (primality check) number = 1(68 times 0)9(6 times 0)21(66 times 0)189 for instance: 1(3 times 0)4 is 10004
frogatto
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If $p_1

If $p_1
Judy Happy
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Is it true that the the odd primes which divide $(2N)^2+3$ is distinct from the ones which divide $(2N)^2+1$?

I have found that the primes which divide $(2N)^2+1$ is of the form $4m+1$. I wonder if it is true that the primes which divide $(2N)^2+3$ is not of the form $4m+1$.
Kim Hollesen
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“… prime numbers p for which $(p)^2$ divides $(p)_3$” — What does $(p)_3$ mean here?

I'm looking at a page at PrimeCurios for the number 9999999900000001, at https://t5k.org/curios/page.php. (Search for that number where it says "Search Curios!") It makes several claims, including this one: 9999999900000001 is the 8th known prime,…
MiguelMunoz
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Possibly repeating pattern in prime numbers

(Read the whole thing) So, I was playing around with prime numbers and found a pattern whith them. It goes like this: First, you write down all numbers ending with 1, 3, 7, and 9, like this: \begin{align} 1001 \\ 1003 \\ 1007 \\ 1009 \\ \\ 1011…
Etscharntmin
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The Prime Explosion: A Visualization of Prime Numbers.

Recently wrote this python demo to show a prime explosion occurring at the origin. Each radiating line represents a prime number, with its length corresponding to the prime's value. The direction each prime takes is random, resulting in a unique…
vengy
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Giving $n$ people a gift with rules below...

Giving $n$ people a gift with rules below... (mark people $1, 2, \cdots, n$ starting from the frontest one.) 1. If $n$ is prime: give "$1$" a gift. 2. Else, for smallest prime $p$ s.t. $p | n$, give $m\cdot p$ a gift. ( $1\leq m \leq \frac n p, m…
RDK
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Condition for a Prime Number

Let there be any prime number $p$. Does it hold that for every $p$ $$(p-1)!=(p-1) \pmod p $$ I came across this condition through trial and error while coding for a function which looks for prime numbers in between two given numbers and applies a…
Aniket Harit
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A pattern in primes numbers?

I created a table to find primes What I did was understand that if you divide every number in half we get a unique number. e.g. 5 is 5/2, and 3 is 3/2, so by including more columns we create a full range of unique identities in a spectrum by…
Larry Revell
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The product of the first $k$ prime numbers except the prime number $2$ $\pm 2$ is a prime number?

If $p_i$ is the $i^{th}$ prime number, let $\forall k \in \mathbb{N}, k>2, P_k := \prod\limits_{i = 2}^{k}p_i.$ Then, at least one of $(P_k + 2, P_k -2)$ is a prime number. I tested it up to $k = 10$. Does it hold for all $k$, really? Is what I'm…
gabriel sobrino
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what is the biggest available (open) DB of prime numbers?

I am having some fun with prime numbers and I am in need of a lot of prime numbers. Maybe I do not need all of them in order.... say, something like this would be enough: What is the 1,000,000th prime? That one (up to the 50,000,000th prime) can be…
eftshift0
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Functional representation of multiples of primes

Given the prime number 7, explain why every multiple of 7 who's factors do not share either 2,3, or 5 can be expressed by the following equations. $ 49 + 210k = y, 77 + 210k = y, 91 + 210k = y, 119 + 210k = y, 133 + 210k = y, 161 + 210k = y, 203 +…
Kevin Perez
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