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Difference between revisions of "Williams prime"

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! Type !! Category !! List<br>table <ref>The list table of any type contains only bases which are included as a separate page.</ref> !! List<br>smallest <ref>The list of smallest primes of any base is an ASCII file for 2 &le; ''b'' &le; 1024. Any unknown value is given with the search range in brackets or empty.</ref>
 
! Type !! Category !! List<br>table <ref>The list table of any type contains only bases which are included as a separate page.</ref> !! List<br>smallest <ref>The list of smallest primes of any base is an ASCII file for 2 &le; ''b'' &le; 1024. Any unknown value is given with the search range in brackets or empty.</ref>
 
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| MM: {{Kbn|(b-1)|b|n}} || [[:Category:Williams prime MM|here]] ||[[Williams prime MM table|here]] || [[:File:Williams prime MM smallest.txt|here]]
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| MM: {{Kbn|(b-1)|b|n}} || [[:Category:Williams prime MM|here]] ||[[Williams prime MM table|here]] || [[Williams prime MM least|here]]
 
|-
 
|-
 
| MP: {{Kbn|+|(b-1)|b|n}} || [[:Category:Williams prime MP|here]] ||[[Williams prime MP table|here]] || [[:File:Williams prime MP smallest.txt|here]]
 
| MP: {{Kbn|+|(b-1)|b|n}} || [[:Category:Williams prime MP|here]] ||[[Williams prime MP table|here]] || [[:File:Williams prime MP smallest.txt|here]]

Revision as of 13:26, 15 May 2019

Definition

A Williams number is a natural number of the form (b-1)bn-1 for integers b ≥ 2 and n ≥ 1.

A Williams prime is a Williams number which is prime.

Generalization

Varying both signs, there're four different types of numbers similiar to Williams numbers.

Lists of primes for bases b and n-values can be found here:

Type Category List
table [1]
List
smallest [2]
MM: (b-1)bn-1 here here here
MP: (b-1)bn+1 here here here
PM: (b+1)bn-1 here here here
PP: (b+1)bn+1 here here here [3]

Notes

  1. The list table of any type contains only bases which are included as a separate page.
  2. The list of smallest primes of any base is an ASCII file for 2 ≤ b ≤ 1024. Any unknown value is given with the search range in brackets or empty.
  3. Values for bases b == 1 mod 3 are always divisible by 3, so not listed here.

External links

Number classes
General numbers
Special numbers
Prime numbers