Difference between revisions of "59"
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| [[satisfies property::irregular prime]] || second irregular prime || {{#lst:irregular prime|list}} || | | [[satisfies property::irregular prime]] || second irregular prime || {{#lst:irregular prime|list}} || | ||
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− | | [[satisfies property::safe prime]] (prime <math>p</math> such that <math>(p-1)/2</math> is also prime) || | + | | [[satisfies property::safe prime]] (prime <math>p</math> such that <math>(p-1)/2</math> is also prime) || sixth safe prime|| {{#lst:safe prime|list}} || <math>(59-1)/2</math> equals [[29]] which is prime. |
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| smaller of a pair of [[twin primes]] || || {{#lst:twin primes|list}} || 59 + 2 = [[61]] which is prime. | | smaller of a pair of [[twin primes]] || || {{#lst:twin primes|list}} || 59 + 2 = [[61]] which is prime. |
Latest revision as of 00:53, 10 July 2013
This article is about a particular natural number.|View all articles on particular natural numbers
Summary
Factorization
The number 59 is a prime number.
Properties and families
Property or family | Parameter values | First few numbers | Proof of satisfaction/membership/containment |
---|---|---|---|
prime number | 17th prime number | 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, [SHOW MORE]View list on OEIS | divide and check |
irregular prime | second irregular prime | 37, 59, 67, 101, 103, 131, 149, 157, 233, 257, 263, [SHOW MORE]View list on OEIS | |
safe prime (prime such that is also prime) | sixth safe prime | 5, 7, 11, 23, 47, 59, 83, 107, 167, [SHOW MORE]View list on OEIS | equals 29 which is prime. |
smaller of a pair of twin primes | 59 + 2 = 61 which is prime. |
Prime-generating polynomials
Below are some polynomials that give prime numbers for small input values, which give the value 59 for suitable input choice.
Polynomial | Degree | Some values for which it generates primes | Input value at which it generates 59 |
---|---|---|---|
2 | all numbers 1-16, because 17 is one of the lucky numbers of Euler. | 7 |