Prime number: Difference between revisions
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{{Wikipedia|Integer factorization}} | {{Wikipedia|Integer factorization}} | ||
By the {{w|fundamental theorem of arithmetic}}, any [[ratio]] can be uniquely represented by a product of prime numbers through prime factorization. It enables the notation of ratios as [[monzo]]s. | By the {{w|fundamental theorem of arithmetic}}, any [[ratio]] can be uniquely represented by a product of prime numbers through prime factorization. It enables the notation of ratios as [[monzo]]s. This is why, in regular temperament theory, prime [[Harmonic|harmonics]] are usually used as the basic building blocks of harmony. | ||
== Prime equal division == | == Prime equal division == | ||
Latest revision as of 03:03, 7 November 2025
A prime number is an integer (whole number) greater than one that is divisible only by itself and one. There are an infinite number of prime numbers, the first few of which are 2, 3, 5, 7, 11, 13, ….
Prime factorization
By the fundamental theorem of arithmetic, any ratio can be uniquely represented by a product of prime numbers through prime factorization. It enables the notation of ratios as monzos. This is why, in regular temperament theory, prime harmonics are usually used as the basic building blocks of harmony.
Prime equal division
A prime equal division is an equal-step tuning that divides a given interval into a prime number of pitches. They are notable because of many interesting properties.
Coprime numbers
Two integers are coprime if they have no divisor in common except 1.
See also
External links
- Die Primzahlseite (German) by Arndt Brünner (helpful tools for prime factorization and ~test)