Elementary properties: subh. name
Okumaya devam et...
← Previous revision | Revision as of 01:20, 9 May 2024 |
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| == Characterizations of the number == | == Characterizations of the number == |
| === Elementary properties === | === Principal properties === |
| '''Five''' is the third-smallest [[prime number]], and the second [[super-prime]], since its prime [[Sequence|index]] is prime.<ref name=":superp">{{Cite web|last=Weisstein|first=Eric W.|title=5|url=https://mathworld.wolfram.com/5.htm...-30|website=mathworld.wolfram.com|language=en}}</ref> Notably, 5 is equal to the sum of the ''only'' consecutive primes [[2]] + [[3]] and it is the only number that is part of more than one pair of [[twin prime]]s, ([[3]], 5) and (5, [[7]]).<ref>{{Cite OEIS |A001359 |Lesser of twin primes. |access-date=2023-02-14 }}</ref><ref>{{Cite OEIS |A006512 |Greater of twin primes. |access-date=2023-02-14 }}</ref> It is the first [[balanced prime]] with equal-sized prime gaps (of 2) above and below it,<ref>{{Cite OEIS |A006562 |Balanced primes (of order one): primes which are the average of the previous prime and the following prime. |access-date=2023-02-14 }}</ref> the first [[safe prime]]<ref>{{Cite OEIS |A005385 |Safe primes p: (p-1)/2 is also prime |access-date=2023-02-14 }}</ref> where <math>(p - 1)/2</math> for a prime <math>p</math> is also prime ([[2]]), and the first [[good prime]], since it is the first prime number whose square ([[25 (number)|25]]) is greater than the product of any two primes at the same number of positions before and after it in the sequence of primes.<ref>{{Cite OEIS|1=A028388 |2=Good primes|access-date=2016-06-01}}</ref> [[11 (number)|11]], the fifth prime number, is the next good prime. 5 forms the first pair of [[sexy prime]]s with 11,<ref>{{Cite OEIS |A023201 |Primes p such that p + 6 is also prime. (Lesser of a pair of sexy primes.) |access-date=2023-01-14 }}</ref> which also the fifth [[Heegner number]],<ref>{{Cite OEIS |A003173 |Heegner numbers: imaginary quadratic fields with unique factorization (or class number 1). |access-date=2023-06-20 }}</ref> and the first [[repunit prime]] in [[Base ten|decimal]], a base in-which five is also the first non-trivial 1-[[automorphic number]].<ref>{{Cite OEIS |A003226 |Automorphic numbers: m^2 ends with m. |access-date=2023-05-26 }}</ref> | '''Five''' is the third-smallest [[prime number]], and the second [[super-prime]], since its prime [[Sequence|index]] is prime.<ref name=":superp">{{Cite web|last=Weisstein|first=Eric W.|title=5|url=https://mathworld.wolfram.com/5.htm...-30|website=mathworld.wolfram.com|language=en}}</ref> Notably, 5 is equal to the sum of the ''only'' consecutive primes [[2]] + [[3]] and it is the only number that is part of more than one pair of [[twin prime]]s, ([[3]], 5) and (5, [[7]]).<ref>{{Cite OEIS |A001359 |Lesser of twin primes. |access-date=2023-02-14 }}</ref><ref>{{Cite OEIS |A006512 |Greater of twin primes. |access-date=2023-02-14 }}</ref> It is the first [[balanced prime]] with equal-sized prime gaps (of 2) above and below it,<ref>{{Cite OEIS |A006562 |Balanced primes (of order one): primes which are the average of the previous prime and the following prime. |access-date=2023-02-14 }}</ref> the first [[safe prime]]<ref>{{Cite OEIS |A005385 |Safe primes p: (p-1)/2 is also prime |access-date=2023-02-14 }}</ref> where <math>(p - 1)/2</math> for a prime <math>p</math> is also prime ([[2]]), and the first [[good prime]], since it is the first prime number whose square ([[25 (number)|25]]) is greater than the product of any two primes at the same number of positions before and after it in the sequence of primes.<ref>{{Cite OEIS|1=A028388 |2=Good primes|access-date=2016-06-01}}</ref> [[11 (number)|11]], the fifth prime number, is the next good prime. 5 forms the first pair of [[sexy prime]]s with 11,<ref>{{Cite OEIS |A023201 |Primes p such that p + 6 is also prime. (Lesser of a pair of sexy primes.) |access-date=2023-01-14 }}</ref> which also the fifth [[Heegner number]],<ref>{{Cite OEIS |A003173 |Heegner numbers: imaginary quadratic fields with unique factorization (or class number 1). |access-date=2023-06-20 }}</ref> and the first [[repunit prime]] in [[Base ten|decimal]], a base in-which five is also the first non-trivial 1-[[automorphic number]].<ref>{{Cite OEIS |A003226 |Automorphic numbers: m^2 ends with m. |access-date=2023-05-26 }}</ref> |
Okumaya devam et...