Alkuluvun

Alkuluvun is the genitive singular form of the Finnish word alkuluku, meaning prime number. In mathematical Finnish, alkuluvun is used when indicating possession or relation to a prime number, for example in phrases like alkuluvun ominaisuudet (the properties of a prime number) or alkuluvun jakajat (the divisors of a prime number).

In number theory, 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 so on. All primes greater than 2 are odd. Prime numbers are fundamental in mathematics because every integer greater than 1 can be factored uniquely into prime numbers, a statement known as the fundamental theorem of arithmetic. It also follows that there are infinitely many prime numbers, a fact established long ago and central to analytic and computational number theory. The distribution of primes is irregular but follows broad patterns described by results such as the prime number theorem.

Finnish mathematical terminology related to alkuluvu is mettere include alkutekijä (prime factor) and faktorisointi (factorization). The plural form alkuluvut means “prime numbers,” while alkuluku denotes a single prime number. The genitive plural is alkulukujen.

Overall, alkuluvun denotes reference to a prime number in possessive or relational contexts, while the broader concept of prime numbers underpins core ideas in algebra, factorization, and number theory.