Primtallet

Primtallet, in Norwegian, refers to a prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The smallest primes are 2, 3, 5, 7, and 11, with 2 being the only even prime.

Important properties include that every integer greater than 1 is either a prime or a product of primes, and this factorization is unique (the fundamental theorem of arithmetic). The number 1 is not considered prime. Primes are distributed irregularly among the natural numbers, but their overall behavior is described by deep results such as the prime number theorem, which states that the number of primes less than x is asymptotically x divided by the natural logarithm of x. A practical method to find primes up to a bound is the Sieve of Eratosthenes, an ancient and efficient algorithm.

Historically, Euclid proved that there are infinitely many primes, a result that underpins much of number theory. Primes are central in mathematics and have important real-world applications, especially in cryptography. Modern public-key systems, such as RSA, rely on the properties of large primes and on the computational difficulty of factoring products of primes.

In Norwegian mathematical usage, primtallet typically refers to the definite singular form “the prime number,” while primtall denotes the general plural concept of prime numbers. As such, primtallet is a key term in discussions of number theory and mathematical foundations.