Hilberttal: Skillnad mellan sidversioner

Innehåll som raderades Innehåll som lades till

Inline

Versionen från 20 december 2013 kl. 12.39

Hilberttal, uppkallat efter David Hilbert, definieras som ett positivt heltal på formen 4n + 1 (Flannery & Flannery (2000, sid. 35)).

De första Hilberttalen är:

1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 181, 185, 189, 193, 197, 201, 205, 209, 213, 217, 221, 225, 229, 233, 237, … (talföljd A016813 i OEIS)

Hilbertprimtal är Hilberttal som inte är delbara med något mindre Hilberttal (med undantag av 1). Observera att Hilbertprimtal inte behöver vara primtal. Till exempel är 21 ett sammansatt tal men ändå ett Hilbertprimtal. Det framgår av multiplikation modulo 4 att ett Hilbertprimtal antingen är ett primtal på formen 4n + 1 (som kallas Pythagoreiska primtal), eller ett semiprimtal på formen (4a + 3) × (4b + 3).

De första Hilbertprimtalen är:

5, 9, 13, 17, 21, 29, 33, 37, 41, 49, 53, 57, 61, 69, 73, 77, 89, 93, 97, 101, 109, 113, 121, 129, 133, 137, 141, 149, 157, 161, 173, 177, 181, 193, 197, 201, 209, 213, 217, 229, 233, 237, 241, 249, 253, 257, 269, 277, 281, 293, 301, 309, 313, 317, 321, 329, … (talföljd A057948 i OEIS)

Källor

Den här artikeln är helt eller delvis baserad på material från engelskspråkiga Wikipedia, Hilbert number, 20 december 2013.

Flannery, S.; Flannery, D. (2000), In Code: A Mathematical Journey, Profile Books

Externa länkar

Weisstein, Eric W., "Hilbert Number", MathWorld. (engelska)

@@ Rad 9: / Rad 9: @@
 De första Hilbertprimtalen är:
-:[[5 (tal)|5]], [[9 (tal)|9]], [[13 (tal)|13]], [[17 (tal)|17]], [[21 (tal)|21]], [[29 (tal)|29]], [[33 (tal)|33]], [[37 (tal)|37]], [[41 (tal)|41]], [[49 (tal)|49]], [[53 (tal)|53]], [[57 (tal)|57]], [[61 (tal)|61]], [[69 (tal)|69]], [[73 (tal)|73]], [[77 (tal)|77]], [[89 (tal)|89]], [[93 (tal)|93]], [[97 (tal)|97]], [[101 (tal)|101]], [[109 (tal)|109]], [[113 (tal)|113]], [[121 (tal)|121]], [[129 (tal)|129]], [[133 (tal)|133]], [[137 (tal)|137]], [[141 (tal)|141]], [[149 (tal)|149]], [[157 (tal)|157]], [[161 (tal)|161]], [[173 (tal)|173]], [[177 (tal)|177]], [[181 (tal)|181]], [[193 (tal)|193]], [[197 (tal)|197]], [[201 (tal)|201]], [[209 (tal)|209]], [[213 (tal)|213]], [[217 (tal)|217]], [[229 (tal)|229]], [[233 (tal)|233]], [[237 (tal)|237]], [[241 (tal)|241]], [[249 (tal)|249]], [[253 (tal)|253]], [[257 (tal)|257]], [[269 (tal)|269]], [[277 (tal)|277]], [[281 (tal)|281]], [[293 (tal)|293]], [[301 (tal)|301]], [[309 (tal)|309]], [[313 (tal)|313]], [[317 (tal)|317]], [[321 (tal)|321]], [[329 (tal)|329]],… {{OEIS|A057948}}
+:[[5 (tal)|5]], [[9 (tal)|9]], [[13 (tal)|13]], [[17 (tal)|17]], [[21 (tal)|21]], [[29 (tal)|29]], [[33 (tal)|33]], [[37 (tal)|37]], [[41 (tal)|41]], [[49 (tal)|49]], [[53 (tal)|53]], [[57 (tal)|57]], [[61 (tal)|61]], [[69 (tal)|69]], [[73 (tal)|73]], [[77 (tal)|77]], [[89 (tal)|89]], [[93 (tal)|93]], [[97 (tal)|97]], [[101 (tal)|101]], [[109 (tal)|109]], [[113 (tal)|113]], [[121 (tal)|121]], [[129 (tal)|129]], [[133 (tal)|133]], [[137 (tal)|137]], [[141 (tal)|141]], [[149 (tal)|149]], [[157 (tal)|157]], [[161 (tal)|161]], [[173 (tal)|173]], [[177 (tal)|177]], [[181 (tal)|181]], [[193 (tal)|193]], [[197 (tal)|197]], [[201 (tal)|201]], [[209 (tal)|209]], [[213 (tal)|213]], [[217 (tal)|217]], [[229 (tal)|229]], [[233 (tal)|233]], [[237 (tal)|237]], [[241 (tal)|241]], [[249 (tal)|249]], [[253 (tal)|253]], [[257 (tal)|257]], [[269 (tal)|269]], [[277 (tal)|277]], [[281 (tal)|281]], [[293 (tal)|293]], [[301 (tal)|301]], [[309 (tal)|309]], [[313 (tal)|313]], [[317 (tal)|317]], [[321 (tal)|321]], [[329 (tal)|329]], … {{OEIS|A057948}}
 == Källor ==
@@ Rad 20: / Rad 20: @@
 {{Naturliga tal}}
-[[Kategori:Hilberts problem]]
+[[Kategori:Hilbertproblem]]
 [[Kategori:Heltalsmängder]]