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- ...orm a full rectangle more than one square wide with 11 squares, so 11 is a prime number.]] A '''prime number''' is a [[integer|whole number]] greater than 1 that can be evenly divided18 KB (2,917 words) - 10:27, 30 August 2014
- #Redirect [[Prime number]]26 bytes (3 words) - 16:11, 14 June 2008
- ...nly 23% of the two-digit numbers and 16% of the three-digit numbers. The [[Prime number#Locating primes|trial division method]] provides an intuitive explanation. ...the [[natural logarithm]] of <math>n</math>). The formal statement of the Prime Number Theorem is4 KB (703 words) - 12:02, 13 November 2007
- Creating [[Prime number/Draft]] [[User:David Tribe|David Tribe]] 20:04, 6 May 2007 (CDT)6 KB (905 words) - 23:27, 13 January 2008
- 949 bytes (118 words) - 12:40, 15 January 2008
- #Redirect [[Prime Number Theorem]]34 bytes (4 words) - 16:00, 20 May 2008
- 133 bytes (20 words) - 05:24, 8 July 2008
- ...orm a full rectangle more than one square wide with 11 squares, so 11 is a prime number.]] ...and itself. The first few prime numbers are 2, 3, 5, 7, 11, 13, and 17. A prime number <math>p</math> cannot be factored as the [[multiplication|product]] of two14 KB (2,281 words) - 12:20, 13 September 2013
- 137 bytes (22 words) - 10:56, 13 November 2008
- 12 bytes (1 word) - 12:02, 13 November 2007
- 12 bytes (1 word) - 12:41, 15 January 2008
- {{r|Prime Number Theorem}}225 bytes (28 words) - 13:16, 14 June 2008
- 854 bytes (137 words) - 02:29, 12 November 2008
Page text matches
- {{r|Prime number}}395 bytes (45 words) - 07:44, 11 November 2009
- Any prime number p such that 2p + 1 is also prime.87 bytes (13 words) - 19:31, 4 September 2009
- If <math>p\ </math> is a prime number and <math>2\cdot p + 1</math> is a prime number too, then we call <math>p\ </math> a '''Sophie Germain prime'''. The Sophie277 bytes (42 words) - 15:41, 23 February 2009
- {{rpl|Prime number}}76 bytes (10 words) - 04:30, 24 September 2013
- {{r|Prime Number Theorem}}225 bytes (28 words) - 13:16, 14 June 2008
- ...portant in [[number theory]] for its connection with the distribution of [[prime number]]s.219 bytes (27 words) - 16:59, 13 November 2008
- #REDIRECT [[Prime number]]26 bytes (3 words) - 21:24, 19 April 2010
- #Redirect [[Prime number]]26 bytes (3 words) - 16:10, 14 June 2008
- #Redirect [[Prime number]]26 bytes (3 words) - 16:11, 14 June 2008
- #Redirect [[Prime number]]26 bytes (3 words) - 20:21, 1 April 2008
- {{r|Prime number}}258 bytes (33 words) - 02:29, 8 February 2009
- #Redirect [[Prime Number Theorem]]34 bytes (4 words) - 16:00, 20 May 2008
- * [[Paulo Ribenboim]]. The New Book of Prime Number Records. Springer-Verlag, 1996, ISBN 0-387-94457-5253 bytes (31 words) - 07:56, 26 January 2010
- * [[Paulo Ribenboim]]. The New Book of Prime Number Records. Springer-Verlag, 1996, ISBN 0-387-94457-5253 bytes (31 words) - 07:51, 15 June 2009
- * [[Paulo Ribenboim]]: The New Book of Prime Number Records. Springer-Verlag, 1996, ISBN 0-387-94457-5253 bytes (31 words) - 10:29, 9 November 2009
- * [[Paulo Ribenboim]]. The New Book of Prime Number Records. Springer-Verlag, 1996, ISBN 0-387-94457-5253 bytes (31 words) - 10:33, 9 November 2009
- ...or of two integers involves [[Unique factorization|factoring]] both into [[prime number]]s: Observe that the prime number 2 occurs twice in the factorization of 60, and three times in the factoriza4 KB (570 words) - 18:05, 1 July 2009
- {{r|Prime Number Theorem}} {{r|Prime number}}574 bytes (75 words) - 21:21, 11 January 2010
- ...meter and number theorist [[Euclid]] of [[Alexandria]], states that if a [[prime number]] ''p'' is a [[divisor]] of the [[multiplication|product]] of two [[integer2 KB (322 words) - 12:51, 18 December 2007
- ...rime''' is a composite number that has certain properties in common with [[prime number]]s. ...can test it for properties that all prime numbers share. One property of a prime number is that it is only divisible by one and itself. This is a defining property2 KB (296 words) - 23:58, 20 February 2010
- * If <math> p^n </math> is a power of a prime number, then2 KB (397 words) - 12:24, 14 May 2008
- ...'except for 2 itself''. Then multiples of 3, 5, 7, 11, and so on for every prime number less than or equal to the ''square root'' of ''N'', are crossed out. In thi1 KB (172 words) - 20:13, 7 December 2020
- {{r|Prime number}}438 bytes (57 words) - 20:29, 11 January 2010
- A prime number that divides a product of two integers must divide one of the two integers.127 bytes (20 words) - 07:08, 4 September 2009
- * [[Paulo Ribenboim]]: The New Book of Prime Number Records. Springer-Verlag, 1996, ISBN 0-387-94457-52 KB (267 words) - 07:56, 15 June 2009
- ...ed that if ''n'' is a whole number for which <math> 2^{n} - 1 </math> is [[prime number|prime]], then the number4 KB (677 words) - 19:07, 7 November 2008
- ...nly 23% of the two-digit numbers and 16% of the three-digit numbers. The [[Prime number#Locating primes|trial division method]] provides an intuitive explanation. ...the [[natural logarithm]] of <math>n</math>). The formal statement of the Prime Number Theorem is4 KB (703 words) - 12:02, 13 November 2007
- A natural number (except 1) which has no proper divisor is called ''[[prime number|prime]]'', * If a prime number divides a product ''ab'', and it does not divide ''a'', then it divides ''b3 KB (515 words) - 21:49, 22 July 2009
- * [[Paulo Ribenboim]]. The New Book of Prime Number Records. Springer-Verlag, 1996, ISBN 0-387-94457-51 KB (188 words) - 21:54, 19 February 2010
- * [[Paulo Ribenboim]]. The New Book of Prime Number Records. Springer-Verlag, 1996, ISBN 0-387-94457-51 KB (203 words) - 07:58, 15 June 2009
- * [[Paulo Ribenboim]], ''The New Book of Prime Number Records'' (3 ed.), Springer, 1996, ISBN 0-387-94457-5207 bytes (27 words) - 10:40, 9 November 2009
- * Similarly, a [[finite field]] of [[prime number|prime]] order has only the identity automorphism. ...> of prime power order ''q'', where <math>q = p^f</math> is a power of the prime number ''p'', has the [[Frobenius automorphism]], <math>\Phi: x \mapsto x^p</math>3 KB (418 words) - 12:18, 20 December 2008
- ...s of the module can be constructed. This is analogous to viewing as the [[prime number]]s as building blocks from which all [[whole number]]s can be assembled. L2 KB (371 words) - 00:36, 2 February 2009
- * <math>p^n</math> and <math>2p^n</math> where ''p'' is an odd [[prime number|prime]].2 KB (338 words) - 16:43, 6 February 2009
- *If <math>p\ </math> is a prime number, than <math>p\ </math> divides <math>L_p - 1\ </math>. The converse is fals798 bytes (117 words) - 04:00, 4 March 2008
- ...subgroup]] which has [[Order of a subgroup|order]] which is a power of a [[prime number]], and which is not strictly contained in any other subgroup with the same1 KB (176 words) - 13:55, 7 February 2009
- {{r|Prime number}}474 bytes (61 words) - 19:48, 11 January 2010
- {{r|Prime number}}545 bytes (70 words) - 16:41, 16 July 2011
- {{r|Prime number}}927 bytes (119 words) - 16:24, 11 January 2010
- {{r|Prime number}}2 KB (247 words) - 17:28, 11 January 2010
- {{r|Prime number}}969 bytes (124 words) - 18:42, 11 January 2010
- ...states that every positive whole number can be expressed as a product of [[prime number]]s in essentially only one way. For instance, <math>12=2 \times 2 \times 33 KB (479 words) - 12:12, 9 April 2008
- If the natural number <math>\scriptstyle p\ </math> is a [[prime number]] then it holds that ...divides <math>\scriptstyle V_m(P,Q)-P\ </math> then is <math>m\ </math> a prime number) are individually false and lead to [[Fibonacci pseudoprime|Fibonacci pseud4 KB (776 words) - 20:44, 20 February 2010
- ...' in [[analytic number theory]] is an upper bound on the distribution on [[prime number|prime]]s in an [[arithmetic progression]]. It states that, if <math>\pi(x;1 KB (202 words) - 16:28, 9 December 2008
- {{r|Prime number}}618 bytes (80 words) - 16:24, 11 January 2010
- ...Carmichael numbers may be extended<ref>Paulo Ribenboim, ''The new book of prime number records'', Springer-Verlag (1996) ISBN 0-387-94457-5. P.120</ref> to4 KB (576 words) - 12:00, 1 January 2013
- {{r|Prime number}}260 bytes (35 words) - 17:07, 26 July 2008
- If ''p'' is a [[prime number]] then ''p'' divides <math>\tbinom{p}{k}</math> for every <math>1<k<p\ </ma3 KB (438 words) - 15:03, 30 November 2009
- {{r|prime number}}207 bytes (26 words) - 19:20, 23 June 2009
- {{r|Prime number}}2 KB (262 words) - 19:07, 11 January 2010
- The '''''p''''' '''-adic''' metric, with respect to a given [[prime number]] ''p'', on the field '''Q''' of [[rational number]]s is a [[metric space|m1 KB (168 words) - 12:39, 4 January 2009
- ...ses prime factorizations. Consider the factorizations of 63 and 77 into [[prime number]]s:6 KB (743 words) - 18:42, 2 July 2009
- For a nonnegative integer ''n'' and a prime number ''p'', the exponent <math> e_{p} </math> in the factorization is called the9 KB (1,496 words) - 06:25, 23 April 2008
- ...y set {0,1,...,p-1} under addition and multiplication modulo p, for any [[prime number]] p, is a field. ...eld is taken to be 0. If the characteristic of a field is nonzero, it is a prime number because otherwise, the number <math>1+1+\cdots+1</math>, where the number o3 KB (496 words) - 22:16, 7 February 2010
- ...sidered as acting on [[commutativity|commutative]] algebras or fields of [[prime number|prime]] [[characteristic of a field|characteristic]] ''p''.1 KB (166 words) - 18:17, 16 February 2009
- * The [[Prime Number Theorem]] is equivalent to the statement that the [[von Mangoldt function]]2 KB (254 words) - 08:27, 19 December 2011
- {{r|Prime Number Theorem}}906 bytes (144 words) - 02:25, 12 November 2008
- ...used in the study of [[arithmetic function]]s and yields a proof of the [[Prime number theorem]]. It is an example of a [[Tauberian theorem]]. ...are values of the [[von Mangoldt function]], it is possible to deduce the prime number theorem from the fact that the zeta function has no zeroes on the line <mat2 KB (362 words) - 16:05, 9 November 2008
- {{r|Prime number}}480 bytes (62 words) - 16:24, 11 January 2010
- ...orm a full rectangle more than one square wide with 11 squares, so 11 is a prime number.]] ...and itself. The first few prime numbers are 2, 3, 5, 7, 11, 13, and 17. A prime number <math>p</math> cannot be factored as the [[multiplication|product]] of two14 KB (2,281 words) - 12:20, 13 September 2013
- {{r|Prime number}}704 bytes (91 words) - 19:38, 11 January 2010
- ...umber]] greater than 2 can be expressed as a sum of two (possibly equal) [[prime number]]s''2 KB (340 words) - 23:24, 14 February 2010
- ...orm a full rectangle more than one square wide with 11 squares, so 11 is a prime number.]] A '''prime number''' is a [[integer|whole number]] greater than 1 that can be evenly divided18 KB (2,917 words) - 10:27, 30 August 2014
- ...erty of the sequence of Perrin numbers is, that if <math>p\ </math> is a [[prime number]], then <math>p\ </math> divides <math>P_p\ </math>. The converse is false,828 bytes (104 words) - 04:32, 19 May 2008
- ...is a polynomial whose roots are used to generate [[field extension]]s of [[prime number|prime]] degree ''p'' in [[characteristic of a field|characteristic]] ''p''.2 KB (295 words) - 15:43, 7 December 2008
- *If <math>\ F_p\ </math> is a prime number different from 3, then <math>\ p</math> is prime. (The converse is fa5 KB (743 words) - 13:10, 27 July 2008
- ...ence when it was shown to have a connection with the distribution of the [[prime number]]s. The most important result related to the Riemann zeta function is the (the index ''p'' running through the set of [[prime number]]s).7 KB (1,113 words) - 10:50, 4 October 2013
- ...r vectors in the space can be assembled. This is similar to viewing the [[prime number]]s as building blocks from which [[positive]] [[integer]]s can be assembled3 KB (464 words) - 19:45, 1 December 2008
- Let <math>p</math> be a [[prime number]] and for any non-zero integer <math>a</math> let <math>|a|_p = p^{-n}</mat9 KB (1,446 words) - 08:52, 30 May 2009
- ...ous kinds of predicate is specified, and pseudo-statements as "Caesar is a prime number" are ill-formed. Now, and this is the main point of Carnap's argument, meta ...example in arithmetic, one can decide and prove that "there exists no even prime number larger than 2". On the other hand the question "Are numbers really existing8 KB (1,255 words) - 13:48, 18 February 2024
- * The set of even [[prime number]]s that contains only one element: {2}.10 KB (1,462 words) - 17:25, 25 August 2013
- * The set of even [[prime number]]s that contains only one element: {2}.10 KB (1,462 words) - 17:24, 25 August 2013
- ...mon divisor]] (gcd) of two [[integer]]s. The algorithm does not require [[prime number|prime factorizations]] and runs efficiently even when methods using prime f7 KB (962 words) - 12:05, 3 May 2016
- == Prime number example ==9 KB (1,394 words) - 13:50, 5 August 2010
- between [[prime number|prime]] and composite numbers, and the perfect squares.16 KB (2,562 words) - 00:45, 13 October 2009
- ...t, if a power of 2 is 1 more than a prime number, then the product of that prime number and the previous power of 2 is a perfect number.8 KB (1,314 words) - 11:25, 13 January 2020
- ...given an integer written in [[binary number|binary]], return all of the [[prime number|prime]] factors of that number. A particular question is called an ''insta ...e problem ''IS-COMPOSITE'' determines whether a given integer is ''not'' a prime number (i.e. a [[composite number]]). When ''IS-PRIME'' returns a ''yes'', ''IS-C17 KB (2,637 words) - 13:14, 6 November 2010
- ... Hz was difficult to reproduce in a laboratory owing to 439 being a [[prime number]].<ref name=Cavanagh/>2 KB (343 words) - 10:27, 6 July 2012
- ...weeks in a [[Julian year]]). This set contains many remarkable subsets : [[prime number]]s, [[Fibonacci number]]s, [[perfect number]]s, [[catalan number]]s, etc.11 KB (1,701 words) - 20:07, 1 July 2021
- ...deal domain]] and any positive integer can be written as the products of [[prime number|primes]] in an essentially unique way. This is the [[fundamental theorem o10 KB (1,566 words) - 08:34, 2 March 2024
- ...enotes a method that does not use [[complex analysis]]. For example, the [[prime number theorem]] was first proven in 1896, but an elementary proof was found only The following are examples of problems in analytic number theory: the [[prime number theorem]], the [[Goldbach conjecture]] (or the [[twin prime conjecture]], o27 KB (4,383 words) - 08:05, 11 October 2011
- ...2, although for the fast evaluation <math>N</math> should not have large [[prime number|prime factor]]s.9 KB (1,368 words) - 11:59, 8 September 2020
- ...ust proved about something else), even if it isn't the same theorem as the Prime Number Theorem. Mentioning "the Fundamental Theorem of Arithmetic" makes it clear12 KB (2,084 words) - 15:38, 11 February 2008
- *<math>\mathbb{P}</math>, the set of [[prime number|prime numbers]]17 KB (2,828 words) - 10:37, 24 July 2011
- ; Prime number multiples ...in any row where the second term is a [[prime number]] are multiple of the prime number. For instance, if a row starts with <math>\scriptstyle 1, 23, 253, \cdots <32 KB (4,192 words) - 18:42, 3 March 2024
- Creating [[Prime number/Draft]] [[User:David Tribe|David Tribe]] 20:04, 6 May 2007 (CDT)6 KB (905 words) - 23:27, 13 January 2008
- ...[analytic number theory]] — the branch of mathematics that studies [[prime number]]s using the tools of mathematical analysis. Factorial numbers, considered32 KB (5,024 words) - 12:05, 22 December 2008
- conjectured what amounts to the [[prime number theorem]] and [[Dirichlet's theorem on arithmetic progressions]]. He gave a35 KB (5,526 words) - 11:29, 4 October 2013
- {{rpr|Prime number}} (November 1)10 KB (1,530 words) - 05:06, 8 March 2024
- Definition: a prime number is a natural number having exactly two divisors. (These are 1 and the numbe34 KB (5,174 words) - 21:32, 25 October 2013
- ...clever proof, such as [[Euclid]]'s proof that there are infinitely many [[prime number]]s, and in a numerical method that speeds calculation, such as the [[fast F30 KB (4,289 words) - 16:03, 20 January 2023
- == "prime number" draft nominated for approval == ...le=Prime_number/Draft&oldid=100142551 This version] of the article titled "prime number" has been nominated for approval. [[User:Michael Hardy|Michael Hardy]] 13:544 KB (7,312 words) - 03:09, 8 March 2024
- ...example in arithmetic, one can decide and prove that "there exists no even prime number larger than 2". On the other hand the question "Are numbers really existing15 KB (2,134 words) - 13:48, 18 February 2024
- ...ternal questions. An internal question is a simple case, like "Does a even prime number greater than 2?" He points out that external questions are only meaningful15 KB (2,251 words) - 14:06, 2 February 2023
- ... Hz was difficult to reproduce in a laboratory owing to 439 being a [[prime number]].<ref name=Cavanagh/> The difference between this standard and the French32 KB (5,025 words) - 10:07, 28 February 2024