Currently there may be errors shown on top of a page, because of a missing Wiki update (PHP version and extension DPL3).
Navigation
Topics Help • Register • News • History • How to • Sequences statistics • Template prototypes

Difference between revisions of "Generalized Fermat number 3 1"

From Prime-Wiki
Jump to: navigation, search
(new)
 
m
 
(One intermediate revision by the same user not shown)
Line 3: Line 3:
  
 
{{#dpl:
 
{{#dpl:
|category=Generalized Fermat number 3 1
+
|category=Generalized Fermat number 3 1 Divs
|titlematch=GF Divisor %
 
 
|namespace=
 
|namespace=
 
|resultsheader=Currently there are '''%PAGES%''' factors known.
 
|resultsheader=Currently there are '''%PAGES%''' factors known.
Line 42: Line 41:
 
{{#dpl:
 
{{#dpl:
 
|debug=0
 
|debug=0
|category=Generalized Fermat number {{#explode:{{PAGENAME}}| |-2}} {{#explode:{{PAGENAME}}| |-1}}
+
|category=Generalized Fermat number {{#explode:{{PAGENAME}}| |-2}} {{#explode:{{PAGENAME}}| |-1}} Nums
|titlematch=Generalized Fermat number %
 
|nottitlematch=Generalized Fermat number diffs %
 
 
|order=ascending
 
|order=ascending
 
|ordermethod=sortkey
 
|ordermethod=sortkey
Line 52: Line 49:
 
|resultsheader=<b>There are %PAGES% General Fermat numbers</b>:\n
 
|resultsheader=<b>There are %PAGES% General Fermat numbers</b>:\n
 
}}
 
}}
 +
{{Navbox Generalized Fermat numbers}}
 
[[Category:Generalized Fermat number 3 1| ]]
 
[[Category:Generalized Fermat number 3 1| ]]

Latest revision as of 22:53, 10 September 2021

Factorizations and statistics of Generalized Fermat numbers GF(3,1) = 32n+1 div 2 and their factors k•2n+1.

Currently there are 121 factors known.

Count of factors according to difference n - m

n-m 2 3 4 5 6 7 8 9 10 11 12
Frequency 23 18 16 6 7 2 1 1 0 1 0

Factorizations

There are 15 General Fermat numbers:

m State Factorization
0 PR 2
1 PR 5
2 PR 41
3 FF 17 * 193
4 PR 21523361
5 PR 926510094425921
6 PR 1716841910146256242328924544641
7 FF 257 * 275201 * 138424618868737<15> * 3913786281514524929<19> * 153849834853910661121<21>
8 FF 12289 * 8972801 * 891206124520373602817<21>
9 FF 134382593 * 22320686081<11> * 12079910333441<14> * 100512627347897906177<21>
15 CF 65537 * 786433 * 3041503300933451777<19> * 951901181416549122049<21> * C<15584>
207 UF 2468256835981809063232453773836025757474103798450369795022913537<64>
34346 UF P<10341>
42290 UF P<12733>
16408814 UF P<4939547>
Generalized Fermat numbers
Miscellaneous
Fermat numbers
Gen. Fermat primes
Gen. Fermat primes
Gen. Fermat primes
categories
GF Divisors