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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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Choosing set of prime numbers

For a given positive integer $ 0 < n < 512$ and $l \,(l < n)$. Is to possible to find set of $n$ prime number such that choosing any $l$ prime numbers without repetition their sums or any basic math operation will not be equal unless the selected…
letsBeePolite
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Is there a way to predict the difference between two primes based on previous differences

If we know the difference between for instance $5-3=2$ and if we also know the difference between $7-5=2$, can we then predict the difference between $X-7=$? Where $X = 11$. Is there an equation/algorithm that can predict the difference without…
Simon
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Prime number sequence?

I was messing around with numbers, trying to find patterns, and came across this one: 91 isn't prime, 991 is, 9991 isn't, 99991 is... If you keep adding 9's, does this pattern hold infinitely?
Tom
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"every prime number $p$ $(p>3)$ can be expressed sum of consecutive numbers " is it true?

I'm finding some necessary and sufficient conditions for a integer $n$ to be a prime number. But I'm not sure if "every prime number $p \, ,(p>3)$ can be expressed sum of consecutive number" is true. If it is right, I hope you help me prove that.…
Thu Le
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What should I do with a new method to find prime numbers?

I may found a new way to find prime numbers (I haven't found anything similar to my method after lots of searching on the internet). I've been able to use it successfully on digits up to 20 digits long but I don't know where to go from here. I know…
Samantha Clark
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How to prove a known prime counting function asymptotic

I saw somewhere that $L(N) = \sum_{i=2}^N \frac{1}{\log(i)}=\pi(N) (1 + o(1))$ as a consequence of Prime Number Theorem. How to prove this? I think I have to prove that $$\lim_{n \to \infty}\frac{L(N) - \pi(N)}{\pi(N)} = 0$$ using the fact that…
C Marius
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I want to find integer soutions to p=(n^2-1)/m^2 where p is a prime number

I want to find all integer solutions for m and n such that $p=\frac{n^2-1}{m^2}$, where p is a prime number as an example, I plugged in p=3 in wolfram and I got that the following values of m and n would work $m=\pm…
Alosapien
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last digit of four consecutive primes

Since two consecutive primes ending in the same last digit has a probability less than mere chance, then four consecutive primes ending in the digits $1,3,7,9$ in any order will be greater than chance. Examples of four primes ending in the four…
J. M. Bergot
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Does r have a solution in $\mathbb{Z}$ here?

Let $a_1,a_2 \in \mathbb{N}$ = $\{1,2,3...\}$ and let p be a prime. If $a_1$ and $a_2$ are co-primes to p, does the equation: $r = \frac{a_1a_2}{p}$ have a solution in $\mathbb{Z}$ here? And how do I sufficiently answer that it hasn't?
Mathaniel
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Relatively prime numbers proof.

How do I rather quickly prove that $$a=2500137802, b=1420515313, c=3920653117$$ are relatively prime numbers? I know it has something to do with Euclidean algorithm, but still doesn't ring a bell to me.
John Robbers
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$p$ is prime and $n \in \mathbb N$ then $p^{n+1} \ne n$

Why is it true that if $p$ is prime and $n \in \mathbb N$ then $p^{n+1} \ne n$
Mano Mini
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Find an $n$ for which $(P_1,\dots,P_n)+1$ is not prime

Q.To show that the number $N=(P_1....P_n)+1$ is not always prime (where $P_1,...,P_n$)are the first n primes) , find an n for which $(P_1...P_n)+1$ is not prime My attempt since $P_1,...,P_n$are the first n primes so $P_1=2$ so product is even so N…
Abdelrhman Fawzy
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How many combinations of $\left ( a,b,c \right )$ are there that makes $a^\left ({b^{c}} \right )$ a prime number

$a,b$ and $c$ are all digits. How many different combinations of $\left ( a,b,c \right )$ are there that makes $a^\left ({b^{c}} \right )$ a prime number? Obviously $a$ has to be $2,3,5$ or $7$ and $b^{c}$ must equal $1$. When $b=1$, $c$ can be…
SarpSTA
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What is the range of integers that only have prime factors of a prime, $p$, or less?

For a prime $p_1$ is there an expression, in terms of $p_1$, for a point at which integers may have a prime factor greater than $p_1$? Also, is it true that for a prime $p_2$, no integers less than ${p_2}^2$ have a prime factor of $p_2$?
ketchupcoke
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Primes of the form $a^k + b^k$

How many primes are there of the form $a^{k/2} + b^{k/2}$ exist for $a$ and $b$ (positive integer solutions). I am hoping there is only one. EDIT $k > 1$
fosho
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