Prime number
A prime number (or a prime) is a natural number 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 n...
Prime number - Wikipedia
Mathematicians Discover Prime Conspiracy
A previously unnoticed property of prime numbers seems to violate a longstanding assumption about how they behave.
Prime number with 22 million digits is the biggest ever found
The Great Internet Mersenne Prime Search has turned up another largest known prime, beating the previous record holder by nearly 5 million digits
Fundamental theorem of arithmetic
In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 either is prim...
Euclid's theorem
Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers. There are several well-known proofs of the theorem.
Euclid offered the follo...
Euclid's theorem - Wikipedia
Integer factorization
In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these integers are further restricted to prime numbers, the process is called ...
Prime number theorem
In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common...
Prime number theorem - Wikipedia
Riemann hypothesis
In mathematics, the Riemann hypothesis, proposed by Bernhard Riemann (1859), is a conjecture that the non-trivial zeros of the Riemann zeta function all have real part 1/2. The name is also ...
Riemann hypothesis - Wikipedia
Modular arithmetic
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus. The modern approach to modular arithmetic was develop...
Public-key cryptography
Public-key cryptography, also known as asymmetric cryptography, is a class of cryptographic algorithms which requires two separate keys, one of which is secret (or private) and one of which is public....
Public-key cryptography - Wikipedia
Prime element
In mathematics, specifically in abstract algebra, a prime element of a commutative ring is an object satisfying certain properties similar to the prime numbers in the integers and to irreducible polyn...
Irreducible element
In abstract algebra, a non-zero non-unit element in an integral domain is said to be irreducible if it is not a product of two non-units.
Irreducible elements should not be confused with prime ele...
Prime ideals
In algebra, a prime ideal is a subset of a ring that shares many important properties of a prime number in the ring of integers. The prime ideals for the integers are the sets that contain all the mu...
Prime ideals - Wikipedia
Primality test
A primality test is an algorithm for determining whether an input number is prime. Amongst other fields of mathematics, it is used for cryptography. Unlike integer factorization, primality tests do no...
Sierpinski number
In number theory, a Sierpinski or Sierpiński number is an odd natural number k such that k2 + 1 is composite, for all natural numbers n. In 1960, Wacław Sierpiński proved that there are infinitely man...
Dickson's conjecture
In number theory, a branch of mathematics, Dickson's conjecture is the conjecture stated by Dickson (1904) that for a finite set of linear forms a1 + b1n, a2 + b2n, ..., ak + bkn with bi ≥ 1, the...
Dickson's conjecture - Wikipedia
Gigantic prime
A gigantic prime is a prime number with at least 10,000 decimal digits. The term appeared in Journal of Recreational Mathematics in the article "Collecting gigantic and titanic primes" (1992) by Samue...
Elliptic curve primality testing
In mathematics elliptic curve primality testing techniques are among the quickest and most widely used methods in primality proving. It is an idea forwarded by Shafi Goldwasser and Joe Kilian in 1986 ...
Elliptic curve primality testing - Wikipedia
SuperPrime
SuperPrime is a computer program used for calculating the primality of a large set of positive natural numbers. Because of its multi-threaded nature and dynamic load scheduling, it scales excellently ...
Fürstenberg's proof of the infinitude of primes
In number theory, Hillel Furstenberg's proof of the infinitude of primes is a celebrated topological proof that the integers contain infinitely many prime numbers. When examined closely, the proof is...
Table of prime factors
The tables contain the prime factorization of the natural numbers from 1 to 1000.When n is a prime number, the prime factorization is just n itself, written in bold below.The number 1 is called a unit...
Wieferich pair
In mathematics, a Wieferich pair is a pair of prime numbers p and q that satisfyWieferich pairs are named after German mathematician Arthur Wieferich.Wieferich pairs play an important role in Preda Mi...
Prime gap
A prime gap is the difference between two successive prime numbers. The n-th prime gap, denoted gn or g(pn) is the difference between the (n + 1)-th and the n-th prime numbers, i.e.We have g...
Prime gap - Wikipedia
PrimeGrid
PrimeGrid is a distributed computing project for searching for prime numbers of world-record size. It makes use of the Berkeley Open Infrastructure for Network Computing (BOINC) platform. As of July 2...
The Music of the Primes
The Music of the Primes (British subtitle: Why an Unsolved Problem in Mathematics Matters; American subtitle: Searching to Solve the Greatest Mystery in Mathematics) is a 2003 book by Marcus du Sautoy...
The Music of the Primes - Wikipedia