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In mathematics, the prime number theorem (PNT) ... increases without bound. For example, the 2 × 10 17 th prime number is 8 512 677 386 048 191 063, [4] and (2 ...
[1] Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example, rational numbers), or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry).
In the geometry of numbers, the subspace theorem was obtained by Wolfgang M. Schmidt in 1972. [6] It states that if n is a positive integer, and L 1,...,L n are linearly independent linear forms in n variables with algebraic coefficients and if ε>0 is any given real number, then the non-zero integer points x in n coordinates with
Theorem — If is a prime number that divides the product and does not divide , then it divides . Euclid's lemma can be generalized as follows from prime numbers to any integers. Theorem — If an integer n divides the product ab of two integers, and is coprime with a , then n divides b .
Takagi existence theorem is a theorem in class field theory. totient function See Euler's totient function. twin prime A twin prime is a prime number that is 2 less or 2 more than another prime number. For example, 7 is a twin prime, since it is prime and 5 is also prime.
Pages in category "Theorems about prime numbers" The following 31 pages are in this category, out of 31 total. ... Prime number theorem; Proth's theorem; R.
Although the proof of Dirichlet's Theorem makes use of calculus and analytic number theory, some proofs of examples are much more straightforward. In particular, the proof of the example of infinitely many primes of the form 4 n + 3 {\displaystyle 4n+3} makes an argument similar to the one made in the proof of Euclid's theorem (Silverman 2013).
Price's theorem (general relativity) Prime number theorem (number theory) Primitive element theorem (field theory) Principal axis theorem (linear algebra) Principal ideal theorem (algebraic number theory) Prokhorov's theorem (measure theory) Proper base change theorem (algebraic geometry) Proth's theorem (number theory)