307 (number): Difference between revisions

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{{AFC submission|r||u=ReyP02|ns=118|reviewer=Doric Loon|reviewts=20231115120948|ts=20231115020730}} <!-- Do not remove this line! -->
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{{AFC comment|1=The concerns from the previous review have not been addressed. The subject of the draft needs to have [[WP:SIGCOV|significant coverage]] in [[WP:RS|reliable sources]] in order to show its [[WP:N|notability]]. Please act on this feedback before submitting again to avoid the draft being rejected. Thanks! <span class="nowrap">—[[User:TechnoSquirrel69|TechnoSquirrel69]]</span> ([[User talk:TechnoSquirrel69|sigh]]) 02:10, 7 November 2023 (UTC)}}

{{AFC comment|1=Fails [[WP:NUMBER]] [[User:Cocobb8|'''<span style="color:purple">Coco</span><span style="color:green">bb8</span>''']] (💬 [[User talk:Cocobb8|talk]] • ✏️ [[Special:Contributions/Cocobb8|contribs]]) 19:25, 5 November 2023 (UTC)}}

{{AFC comment|1=First ref doesn't mention the subject and all the others are merely passing mentions. [[User:Stuartyeates|Stuartyeates]] ([[User talk:Stuartyeates|talk]]) 20:41, 4 November 2023 (UTC)}}

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{{Draft topics|mathematics}}
{{AfC topic|stem}}

{{Infobox number
{{Infobox number
| number = 307
| number = 307
| divisor = 1, 307
| prime = 63rd | divisor = 1, 307
}}
}}


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==In mathematics==
==In mathematics==
*307 is an odd [[prime number]].<ref>{{Cite web |url=https://mathworld.wolfram.com/PrimeNumber.html|title=Prime number information|website=mathworld.wolfram.com}}</ref>
*307 is the 63rd prime number and an odd [[prime number]].<ref>{{Cite web |url=https://mathworld.wolfram.com/PrimeNumber.html|title=Prime number information|website=mathworld.wolfram.com}}</ref> It is an isolated (i.e., not [[Twin prime|twin]]) prime,<ref>{{Cite OEIS|A007510|Single (or isolated or non-twin) primes: Primes p such that neither p-2 nor p+2 is prime}}</ref> but because 309 is a [[semiprime]], 307 is a [[Chen prime]].<ref>{{Cite OEIS|A109611|Chen primes: primes p such that p + 2 is either a prime or a semiprime}}</ref><ref>{{Cite arXiv|title=Chen primes in arithmetic progressions|first=Pawel|last=Lewulis|date=2016 |class=math.NT |eprint=1601.02873 }}</ref>
⚫
*307 is the number of one-sided [[Polyiamond|noniamonds]] meaning that it is the number of ways to organize 9 triangles with each one touching at least one other on the edge.<ref>{{Cite OEIS|A006534|Number of one-sided triangular polyominoes (n-iamonds) with n cells; turning over not allowed, holes are allowed}}</ref>
*307 is a [[Chen prime]] number meaning that 309 is either [[Prime number|prime]] or [[semiprime]].<ref>{{Cite OEIS|A109611|Chen primes: primes p such that p + 2 is either a prime or a semiprime}}</ref><ref>{{Cite web|url=https://arxiv.org/pdf/1601.02873.pdf|website=arxiv.org|title=Chen primes in arithmetic progressions|first=Pawel|last=Lewulis}}</ref>
⚫
*307 is the number of one-sided [[Polyiamond|octiamonds]] meaning that it is the number of ways to organize 8 triangles with each one touching at least one other on the edge.<ref>{{Cite OEIS|A006534|Number of one-sided triangular polyominoes (n-iamonds) with n cells; turning over not allowed, holes are allowed}}</ref>
*307 is the third non-palindromic number to have a [[Palindromic number|palindromic]] [[square number|square]]. 307<sup>2</sup>=94249.<ref>{{Cite OEIS|A028818|Palindromic squares with odd number of digits and non-palindromic and "non-core" square roots}}</ref>
*307 is the third non-palindromic number to have a [[Palindromic number|palindromic]] [[square number|square]]. 307<sup>2</sup>=94249.<ref>{{Cite OEIS|A028818|Palindromic squares with odd number of digits and non-palindromic and "non-core" square roots}}</ref>
*307 is the number of [[solid partition]]s of 7.<ref>{{Cite OEIS|A000293|a(n) {{=}} number of solid (i.e., three-dimensional) partitions of n}}</ref>
*307 is a [[Central polygonal numbers|central polygonal number]] meaning that it follows the equation x<sup>2</sup>-n+1<ref>{{Cite OEIS|A002061|Central polygonal numbers: a(n) = n^2 - n + 1}}</ref><ref>{{Cite web|url=https://tomrocksmaths.files.wordpress.com/2021/05/teddyrockshenrikhelsen.pdf|website=tomrocksmaths.files.wordpress.com|title=Central Polygonal Numbers|first=Henrik|last=Helsen}}</ref>
*307 is one of only 16 natural numbers for which the [[imaginary quadratic field]] <math>\mathbb{Q}(\sqrt{-n})</math> has [[Class number (number theory)|class number]] 3.<ref>{{Cite OEIS|A006203|Discriminants of imaginary quadratic fields with class number 3 (negated)}}</ref>


==Other fields==
== References ==
*The calendar years [[307|307 AD]] and [[307 BC]].
*307 is the number for several [[list of highways numbered 307|highways]] across the countries of [[Brazil]], [[Canada]], [[China]], [[Costa Rica]], [[India]], [[Japan]], [[Mexico]], the [[Philippines]], the [[United Kingdom]], and the [[United States]]. For example the [[Bundesstraße 307]] in [[Germany]].


== References ==
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{{reflist}}
{{reflist}}
{{Integers|3}}

[[Category:Integers]]

Latest revision as of 20:00, 18 April 2024

← 306 307 308 →
Cardinalthree hundred seven
Ordinal307th
(three hundred seventh)
Factorizationprime
Prime63rd
Divisors1, 307
Greek numeralΤたうΖぜーた´
Roman numeralCCCVII
Binary1001100112
Ternary1021013
Senary12316
Octal4638
Duodecimal21712
Hexadecimal13316

307 is the natural number following 306 and preceding 308.

In mathematics[edit]

References[edit]

  1. ^ "Prime number information". mathworld.wolfram.com.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A007510 (Single (or isolated or non-twin) primes: Primes p such that neither p-2 nor p+2 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A109611 (Chen primes: primes p such that p + 2 is either a prime or a semiprime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^ Lewulis, Pawel (2016). "Chen primes in arithmetic progressions". arXiv:1601.02873 [math.NT].
  5. ^ Sloane, N. J. A. (ed.). "Sequence A006534 (Number of one-sided triangular polyominoes (n-iamonds) with n cells; turning over not allowed, holes are allowed)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ^ Sloane, N. J. A. (ed.). "Sequence A028818 (Palindromic squares with odd number of digits and non-palindromic and "non-core" square roots)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. ^ Sloane, N. J. A. (ed.). "Sequence A000293 (a(n) = number of solid (i.e., three-dimensional) partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  8. ^ Sloane, N. J. A. (ed.). "Sequence A006203 (Discriminants of imaginary quadratic fields with class number 3 (negated))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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