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#REDIRECT [[Twin prime#Twin prime conjecture]] [[Category:Conjectures about prime numbers]] ...

...</sub>)², where ''p''_''n'' is the ''n''^th prime number, for every ''n'' ≥ 2.<ref>{{mathworld|urlname=BrocardsConjecture|tit ! n !! <math>p_n</math> !! <math>p_n^2</math> !! Prime numbers !! <math>\Delta</math> ...

{{Short description|Concatenation of the first n prime numbers}} ...rst ''n'' [[prime number]]s written in that base. Smarandache&ndash;Wellin numbers are named after [[Florentin Smarandache]] and [[Paul R. Wellin]]. ...

...y]], the '''second Hardy–Littlewood conjecture''' concerns the number of [[prime number|primes]] in [[Interval (mathematics)|intervals]]. Along with the [[f ...z'')}} denotes the [[prime-counting function]], giving the number of prime numbers up to and including {{Mvar|z}}. ...

...wood conjecture|Hardy and Littlewood conjecture]] on the density of [[twin prime]]s or their conjecture on primes of the form ''n''²&nbsp;+&nbsp; ...e conjecture is how to give conditions where the values are simultaneously prime for infinitely many ''n''. ...

{{Short description|Prime number conjecture}} ...nt of a set of consecutive [[composite number]]s one can assign a distinct prime that divides it. It was first published in ''[[American Mathematical Monthl ...

...e [[Bernoulli number]]s ''B''_''k'' postulates that ''p'' is a [[prime number]] [[if and only if]] ...ation is due to [[Giuseppe Giuga]], from 1950, to the effect that ''p'' is prime if and only if ...

...tural number]]s [[less than]] any given number have an ''odd'' number of [[prime factor]]s. The [[conjecture]] was set forth by the Hungarian mathematician ...C&pg=PA483}}.</ref> providing an illustration of the [[strong law of small numbers]]. ...

...]] is a small set, and so is any [[geometric progression]] (i.e., a set of numbers of the form of the form ''ab''^''n'' with ''a''&nbsp;≥&nbsp;1, '' ...um of the reciprocals of the primes diverges|is large]]. The set of [[twin prime]]s is small (see [[Brun's constant]]). ...

In [[number theory]], a '''Wagstaff prime''' is a [[prime number]] of the form ...at the Eurocrypt 1990 conference. Wagstaff primes appear in the [[Mersenne conjectures#New Mersenne conjecture|New Mersenne conjecture]] and have applications in ...

...mbers]] that are practicals<ref>{{cite journal|title=A survey on practical numbers |author=Melfi, G. |journal=Rend. Sem. Mat. Torino |volume=53 |year=1995 |pa ...Melfi, G. and Parton, M. ''Primitive abundant and weird numbers with many prime factors'', ...

{{Short description|Conjecture about prime gaps}} ...?id=mdp.39015035450967&view=1up&seq=411 |trans-title=New research on prime numbers |language=French}} ...

{{Short description|There is a prime between any two square numbers}} ...ecture''', proposed by [[Adrien-Marie Legendre]], states that there is a [[prime number]] between <math>n^2</math> and <math>(n+1)^2</math> for every [[posi ...

In [[mathematics]], '''Serre's multiplicity conjectures''', named after [[Jean-Pierre Serre]], are certain problems in [[commutativ ...ve ring|commutative]], [[regular local ring]] and let ''P'' and ''Q'' be [[prime ideal]]s of ''R''. Serre defined the [[intersection multiplicity]] of ''R'' ...

His father, [[Jules de Polignac]] (1780-1847) was prime minister of [[Charles X of France|Charles X]] until the Bourbon dynasty was ...heory|Number Theory]] and he specifically worked with [[Prime number|prime numbers]]. ...

...hsConjecture |title=The Prime Glossary: Gilbreath's conjecture |work=The [[Prime Pages]] |access-date=2008-03-07 |archive-date=2012-03-24 |archive-url=https Gilbreath observed a pattern while playing with the ordered sequence of prime numbers ...

{{About|meaning in the number theory||Covering (disambiguation){{!}}Covering}} ...sequence|sequence of integers]] refers to a [[set (mathematics)|set]] of [[prime number]]s such that ''every'' term in the [[sequence]] is [[divisible]] by ...

{{short description|Number of form 2^(2^p-1)-1 with prime exponent}} In [[mathematics]], a '''double Mersenne number''' is a [[Mersenne prime|Mersenne number]] of the form ...

...\times 2^n + 1 </math> is [[composite number|composite]] for all natural numbers ''n''. In 1960, [[Wacław Sierpiński]] proved that there are [[Infinity|infi ==Known Sierpiński numbers== ...

* [[Serre's multiplicity conjectures]] * [[Homological conjectures]] ...