Search results

{{Short description|Conjecture about prime numbers}} ...ly many positive integers {{mvar|n}} for which they are all [[prime number|prime]], unless there is a [[Modular arithmetic|congruence]] condition preventing ...

{{short description|Existence of a prime number between each square and pronic number}} ...mber and a pronic number (both greater than one) separated by at least one prime?}} ...

...is a [[conjecture]] about the distribution of prime divisors of [[Mersenne numbers]] and was made by [[Donald B. Gillies]] in a 1964 paper<ref>{{cite journal ...is a specialization of the [[prime number theorem]] and is a refinement of conjectures due to [[I. J. Good]]<ref>{{cite journal ...

| caption = Plot showing the number of [[twin prime]]s less than a given ''n''. The first Hardy–Littlewood conjecture predicts ...er of [[prime k-tuple]]s less than a given magnitude by generalizing the [[prime number theorem]]. It was first proposed by [[G. H. Hardy]] and [[John Edens ...

...ion|Dirichlet {{mvar|L}}-function]] for the field of [[Gaussian rational]] numbers. This formula is a special case of the [[analytic class number formula]], a ==Conjectures== ...

...clotomic polynomial]]s (i.e. where the index is the product of three prime numbers). It is named after [[Marion Beiter]], a Catholic nun who first proposed it ...This implies the existence of <math>M(p):=\max\limits_{p\leq q\leq r\text{ prime}}A(pqr)</math> such that <math>1\leq M(p)\leq p-1</math>. ...

Their vertices can be identified with the numbers from 0 to <math>n-1</math>, and two vertices <math>i</math> and <math>j</ma ...onjecture states that, when every member of <math>S</math> is [[relatively prime]] to <math>n</math>, then the only symmetries of the circulant graph for <m ...

{{Short description|Bound on the gaps between prime numbers}} [[File:Wikipedia primegaps.png|thumb|450px|Prime gap function]] ...

then either <math>n</math> is prime or <math>n^2 \equiv 1 \pmod r</math> .../www.cse.iitk.ac.in/users/nitin/talks/Dec2014-3Paris.pdf|title=Primality & Prime Number Generation|last=Saxena|first=Nitin|date=Dec 2014|publisher=UPMC Pari ...

...] for [[Dedekind zeta function]]s, and also of [[Stickelberger's theorem]] about the [[factorization]] of [[Gauss sums]]. It is named after [[Armand Brumer] ...f places of {{math|''k''}} containing the [[Archimedean place]]s and the [[prime ideal]]s that [[Ramification theory of valuations|ramify]] in {{math|''K''/ ...

Let <math>G</math> be a finite group and <math>p</math> a prime. The set <math>{\rm Irr}(G)</math> of irreducible complex [[Character theor ...3–1160 |doi=10.1006/jabr.1996.0304 }}</ref> except for finitely many prime numbers. A proof of the last open cases was published in 2004<ref>{{cite journal |l ...

The complexities of the numbers 1, 2, 3, ... are The smallest numbers with complexity 1, 2, 3, ... are ...

...us; 1}}. [[D. H. Lehmer]] conjectured in 1932 that there are no composite numbers with this property.<ref>Lehmer (1932)</ref> ...rst1=Graeme L. | last2=Hagis | first2=Peter, jun. | title=On the number of prime factors of ''n'' if φ(''n'') divides ''n''−1 | journal=Nieuw Arch. Wiskd. | ...

...m/books?id=wSpgDwAAQBAJ&pg=PA194 |language=en}}</ref> For the statement of conjectures and theorems, technical side conditions and quantifications of complexity a The imaginary exponential function <math>e(x)</math> maps the real numbers to the circle group (see [[Euler's formula#Topological interpretation]]). A ...

...ble complex [[character theory|characters]] of degree not divisible by a [[prime number]] <math>p</math> and the [[order (group theory)|order]] of the [[cen ...r generalized by other mathematicians to a more general conjecture for any prime value of <math>p</math> and more general groups. ...

...the series of subgroups of a finite p-group, ''G'', indexed by the natural numbers: ...'² points is the [[wreath product]] of two [[cyclic group]]s of prime order. When ''p'' = 2, this is just the dihedral group of order 8. It too ...

| title = On the relations of various conjectures on Latin squares and straightening coefficients | title = The conjectures of Alon–Tarsi and Rota in dimension prime minus one ...

{{For|other uniform boundedness conjectures|Uniform boundedness conjecture (disambiguation){{!}}Uniform boundedness con .../math>. Furthermore if <math>P\in E(K)_{\text{tors}}</math> is a point of prime order <math>p</math> we have <math>p\leq d^{3d^2}.</math> ...

{{Short description|Prime number of the form k*(2^n)+1}} |parentsequence=Proth numbers, [[prime numbers]] ...

...uadratic reciprocity. In the first one (1828) he proved Euler's conjecture about the biquadratic character of 2. In the second one (1832) he stated the biqu As is often the case in number theory, it is easiest to work modulo prime numbers, so in this section all moduli ''p'', ''q'', etc., are assumed to positive, ...