Prime numbers

positive integer with exactly two divisors, 1 and itself

positive integer that has at least one positive divisor other than 1 or itself

function representing the number of primes less than or equal to a given number

In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers. Because there are infinitely many prime numbers, there are also infinitely many semiprimes. Semiprimes are also called biprimes, since they include two primes, or second numbers, by analogy with how "prime" means "first". Alternatively semiprimes are called almost-prime numbers, specifically the "2-almost-prime" biprime and "3-almost-prime" triprime.

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a visualization of the prime numbers formed by arranging the integers into a spiral

In mathematics, and more particularly in number theory, primorial, denoted by "p_{n}\#", is a function from natural numbers to natural numbers similar to the factorial function, but rather than successively multiplying positive integers, the function only multiplies prime numbers.

largest prime number that is currently known

the prime number 10³⁰+666×10¹⁴+1

positive integer that is the product of three distinct prime numbers

difference between two successive prime numbers

natural number with a given number of prime factors

positive integer power of a prime number

number k which k*2^n+1 is composite with all n

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number whose decimal representation is the concatenation of "0." with the base 10 representations of the prime numbers in order

Primecoin (Abbreviation: XPM) is a cryptocurrency that implements a proof-of-work system that searches for chains of prime numbers.

odd natural number k such that k·2^n − 1 is composite for all natural n

prime-generating mathematical constant

the identity (a+b)ᵖ = aᵖ + bᵖ, which holds if the prime number p>0 is the characteristic of the ring we work in

the smallest integer which yields a prime number when added to a given primorial

formula whose values are exactly the prime numbers

set of prime numbers linked by a linear relationship

two consecutive integers for which the sums of the prime factors of each are equal

type of sequence of prime numbers

integer obtained by concatenating the first k primes in decimal for some k

A megaprime is a prime number with at least one million decimal digits.

mathematical proof

class of natural numbers

In mathematics, an interprime is the average of two consecutive odd primes. For example, 9 is an interprime because it is the average of 7 and 11. The first interprimes are: 4, 6, 9, 12, 15, 18, 21, 26, 30, 34, 39, 42, 45, 50, 56, 60, 64, 69, 72, 76, 81, 86, 93, 99, ... Interprimes cannot be prime themselves (otherwise the primes would not have been consecutive).

real number whose nth binary digit is 1 if n is prime and 0 if n is composite or 1

phenomenon that most of the time, there are more primes of the form 4k + 3 than of the form 4k + 1, up to the same limit

type of natural number in recreational number theory

tuple describing patterns of differences between prime numbers

infinite sequence of prime numbers

mathematical constant

two theoretical number functions

algorithms to generate prime numbers

43,112,609 (forty-three million, one hundred twelve thousand, six hundred nine) is the natural number following 43,112,608 and preceding 43,112,610.

mathematical problem in number Theory