Template:Proth prime

Description

Template Proth prime

Display of current data for Proth primes k•bⁿ+1, comments will be displayed as references at the bottom.

Prototype

{{Proth prime
|Pk=
|Pb=
|PCount=
|PNash=
|PMaxn=
|PDate=
|PReserved=
|PMultiRes=
|PNlist=
|PRemarks=
|PSieve=
}}

Parameters

• Pk: the k-value of k•bⁿ+1
• Pb: the b-value of k•bⁿ+1
• PCount: the number of n-values given

If no count is given, this will be automatically counted. If given and differs from automated value, a warning will be shown.

• PNash: the Nash weight
• PMaxn: highest n-value of continuous searched range (from n=1)
• PDate: last date of edit (latest history entry)
• PReserved: person(s) who reserved this sequence (comma separated)
• PMultiRes: number of Multi Reservation: PMaxn and PDate will be taken from there
• PNlist: list of every n-value (one per row) with comments
• PRemarks: any helpful text or links for this sequence
• PSieve: if set a zip-file can be uploaded (filename is given then) if not available; if exists file is downloadable

Explanations

In case of the following conditions special categories will be set automatically (b = 2 only):

• k-value is disvisible by 3 → category Proth 3k is set
• k-value is disvisible by 15 → category Proth 15k is set
• k-value is disvisible by 2145 → category Proth 2145k is set
• k-value is disvisible by 2805 → category Proth 2805k is set

Any base:

• Nash-weight < 1000 → category Proth Low-weight is set
• If there are 100 n-values or more → Proth Count-100 is set
• If PCount=0 → category Proth Count 0 is set
• If PCount=0 & PNash=0 & PMaxn=0 → Proth Sierpinski is set

The category Proth prime for base b is set by default.

If "PMultiRes" is set, the parameters "PMaxn", "PDate" and "PReserved" (if given) will be ignored and replaced by the data from the Multi Reservation with ID given.

See also

• Template:K-type

Example

{{Proth prime
|Pk=15
|Pb=2
|PCount=4
|PNash=239
|PMaxn=20
|PDate=2019-03-01
|PReserved=Karsten Bonath
|PMultiRes=
|PNlist=
2;T:ST;C: Testtext
3;T:SW;C:[[Help:Examples|Examples]]
5;C:'''Example'''
15;43912;C:with Top5000 entry
|PRemarks=For this {{Vk}}-value these are the [[Generalized Fermat prime]]s.
|PSieve=y
}}

will create:

Current data

k , b : 15 , 2 Type : 315 Count : 4 Nash : 239 Max n : 20 Date : 2019-03-01 Reserved : Karsten Bonath

2, 3, 5, 15

Remarks :

For this k-value these are the Generalized Fermat primes.