Mathematics Stack Exchange
Mathematics Stack Exchange

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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Do 50% of primes give primes of the form $P=15p+4$?

Do 50% of primes give primes of the form $P=15p+4$? I checked this for primes $p$ form 7 up to 233 and found 21 primes out of 38 produce primes of the form $15p+4$: $(p, P):(7,109), (13,199),(23,349),(29,439),(41, 619), (47, 709), (61, 919), (67,…
sirous
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Why is -1 not a prime number?

I understand the reason 1 is not considered to be a prime number, but what is the reasoning for -1 not being considered a prime number? It's only factors are 1 and itself, -1, wouldn't that make it a prime number?
BobS
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Thinker with no maths knowledge - checking primes

My route for checking whether a number is a prime (>3) is if n-5÷6= whole number or n-7÷6= whole number Is this wrong please? Sue
Sue
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What's the largest prime number found using the Eratosthenes sieve?

Just looking for the number asked in the question. I have a reason for wanting to know. I've googled this question and the closest I have come to an answer is this: "The sieve of Eratosthenes is one of the most efficient ways to find all primes…
PAL
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Can I prove n^2 - n + 1 prime for all even n?

I was playing around with numbers the other day and realized that the first few values for $n(n - 1) + 1$ are prime. Now, I also quickly realized that not all values are prime ($n = 5$ results in 21, which is not prime), but I also noticed that all…
IronEagle
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What will accepting 1 as prime change?

How significant is the fact 1 isn't a prime number? What will happen if it is? What areas of Mathematics are affected by changing the fact? I know why and how 1 isn't a prime. My question is how significant is the fact.
Krishna Deshmukh
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The sum of two prime powers equal a third prime power.

Is $$13^2 + 7^3 = 512=2^9$$ the only solution for the sum of two primes $p,q$ raised to powers greater than $1$ equals a third prime power?
J. M. Bergot
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Function for prime numbers

Is there a a function for calculating nth prime number? A near approximate answer would also do as I need for numbers below 1000.
Atharva Kathale
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Is there any pattern in prime numbers

Do a pattern exist in set of prime numbers or is there any expression for a prime number?? I am unable to find any relation between prime numbers
vishesh das
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Pairs of Consecutive Primes

In August 2014, Polymath group showed that subject to the generalized Elliott–Halberstam conjecture, one can show the existence of infinitely many pairs of consecutive primes that differ by at most 6. The list of primes less than 100 shows that…
StopReadingThisUsername
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Co-prime number list.

I need to make an infinite sequence of natural numbers which contains no prime numbers, yet any pair of them are co-prime with each other. I tried just finding numbers between 1 - 100 that forms a co-prime list, but couldn't find a pattern or rule…
User426190
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Can we extend and generalise the ruler function by using only powers of $-1$ or other "simple" means, to calculate primality?

Can we extend and generalise the ruler function by using only powers of $-1$ or other "simple" means, and then sum over the primes to efficiently test primality? The ruler function (let's call it $r(n)$) is the exponent of the largest power of 2…
it's a hire car baby
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PRIME NUMBER is the relation given always true or is it false, $2^n-1$

If n is a prime no. Is it necessary that $2^n - 1$ is also a prime no. I know that the converse is true, but i want to know about this statement. If it's wrong plz. Give an eg. If its right plz. Prove it.
Display name
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Is there a proof that every prime containing only the digit “1” must have a prime as its digit sum?

Verbal proof is preferred as I'm not to familiar with mathematical notation.
knowbuddy
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Proof for whether or not a function will ever be non-prime.

From the proof that there are infinitely many primes: Given all the primes $p_i$ known up to the $n$th prime, construct the number $q_n$ such that $$ q_n = 1 + \prod^{n}_{i=1} p_i $$ Since there is no prime within the first $n$ primes that evenly…
Axoren
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