cikakkun lambobi

cikakkun lambobi a lissafi

Lissafi ya wanzu tun farkon. Idan za a yi imani da gano kashi na Ishango (shekaru 20.000 da suka wuce), yana iya zama hujja ta farko ta sanin manyan lambobi da yawa na farko, amma batun ya ci gaba da haifar da cece-kuce. Yayin da lissafi ya kasance asiri ga yawancin mu, wasu suna ganin shi a matsayin babbar hanya ta fahimta da kuma nazarin duniya. A cikin ilimin lissafi akwai cikakkun lambobiWani abu da mutane da yawa ba su sani ba.

A cikin wannan labarin za mu gaya muku duk abin da kuke buƙatar sani game da cikakkun lambobi da halayen su.

menene cikakkun lambobi

shida lamba

Cikakkun lambobi duk game da nemo abubuwan farko na Mersenne. A haƙiƙa, Shawara ta 36 na Littafi na IX na Abubuwan Euclid ta ce idan lambar Mersenne 2n – 1 ta zama firam, to 2n-1 (2n – 1) cikakkiyar lamba ce.

René Descartes ya tabbatar a cikin wata wasika zuwa ga Mason cewa kowane lamba ko Euclid ne, amma bai tabbatar da ka'idarsa ba. Maimakon haka, masanin lissafin Swiss Leonhard Euler Shi ne na farko da ya nuna abin lura na Cartesian. Haɗuwa da sakamakon Euclid da Euler suna ba da damar samun cikakkiyar sifa na cikakkun lambobi.

An san lambobi cikakke huɗu na farko tun zamanin d ¯ a. Sun bayyana a cikin ayyukan Nico Marcos de Graça da Theon de Smyrna. An ambaci cikakkiyar lamba ta biyar a cikin Lambobin Latin na 1456. Cataldi ya gano lambobi na shida da na bakwai a cikin karni na XNUMX. kuma na takwas na Euler a cikin 1772.

Don haka a farkon shekarun 1950 mun san cikakkun lambobi 12, amma godiya ga GIMPS (Great Internet Mersenne Prime Search), binciken ya haɓaka tare da haɓakar fasaha da kuma amfani da kwamfutoci a cikin 1990s.

Me suke yi

cikakkun lambobi

Idan masu lissafi da yawa suna ɗaukar lambobi masu mahimmanci a matsayin tushen lissafi, to cikakkun lambobi ba su da wani amfani na musamman. tun da ba a yi amfani da su don magance daidaito ba, ƙididdiga ko shigar da yanayin cryptography.

A zamanin d ¯ a, an ɗauka cewa sun fi girma, kuma wani ya ga aikin sufi a cikinsa: "Shida kansa cikakken adadi ne, ba domin Allah ya halicci kome a cikin kwanaki shida ba, amma domin Allah ya halicci kome a cikin kwanaki shida domin adadi cikakke ne." Saint Augustine a cikin birnin Allah (420 AD)

Suna ɗaya daga cikin asirai na lissafin lissafi, kuma neman sabbin lambobi cikakke na ci gaba da burge masana ilimin lissafi da yawa.

Akwai zato da yawa game da cikakkun lambobi. Zato wata ka'ida ce da ba a taɓa tabbatar da ita ba. Ga uku:

  • Cikakken lambobi na Euclid duk ma lambobi ne saboda daya daga cikin abubuwan shine ikon 2. Amma babu wata shaida da ta tabbatar da cewa babu wata cikakkiyar lambobi;
  • Duk sanannun lambobi suna ƙare a 6 ko 28, amma wannan ba koyaushe haka yake ba;
  • Haka kuma ba a tabbatar da cewa lallai akwai lambobi cikakke marasa iyaka ba.

menene cikakkun lambobi

jerin lambobi

Cikakken lambobi ba safai ba ne. Yayin da duk masu ilimin lissafi sun yarda cewa akwai adadi mara iyaka daga cikinsu (ba a taɓa tabbatarwa ba), a yau mun san 50 ne kawai kuma ba za mu iya tabbatar da cewa babu cikakkiyar ma'anar lamba da ba a gano ba tun 47.

An gano cikakkiyar lamba ta ƙarshe a cikin Janairu 2018. Gano sabon babban firam ɗin yana nufin gano sabuwar cikakkiyar lamba, wanda shine gano lamba 2⁷⁷²³²⁹¹⁷-1.

Akwai cikakkun lambobi guda uku da suka kasa da 1000: 6, 28 da 496. A fili ko da cikakken lambobi sun ƙare a 6 ko 8, kodayake ba a taɓa tabbatar da hakan ba, ba koyaushe haka lamarin yake ba.

Madaidaitan lambobi a cikin dabarar 2n-1 (2n – 1) lambobi ne masu kusurwa uku (ko ma hexagonal). A gefe guda, duk hatta lambobi banda na farko daidai ko da lamba shine jimlar 2(n-1)/2 cubes na lambobi marasa kyau na farko. Misali:

  • = 28 13+ 33,
  • = 496 13+ 33 + 53 + 73,
  • = 8128 13+ 33 + 53 + 73 + 93 + 113 + 133 + 153.

Lambobi cikakke takwas na farko sune:

  • 6
  • 28
  • 496
  • 8128
  • 336
  • 869.056
  • 691.328
  • 2 305 843 008 139 952 128.

Wasu tarihin

Saint Augustine, wanda kuma aka sani da Augustine na Hippo (354-430), fShi masanin Falsafa ne, marubuci, masanin lissafi, kuma firist. Idan ka yi nazari a kan batun falsafa, sunan zai saba maka, tun da yana daya daga cikin masana falsafa da suka saba nazarin wannan batu. Kamar sauran haziƙai na zamaninsa, Saint Augustine yana ɗaya daga cikin waɗanda suka haɓaka da zurfafa ilimi a fagagen da suka fara daga falsafa zuwa lissafi, tare da ganin abubuwa da yawa fiye da yadda muke zato a yau.

To, Augustine na Hippo ya ce cikakken lambobi suna da dalilin wanzuwa. A cikin aikinsa na birnin Allah, ya bayyana cewa 6 cikakke ne domin Allah ya halicci duniya a cikin kwanaki shida. Lamba na gaba, 28, yayi daidai da adadin kwanakin da wata ke ɗauka don kewaya duniya sau ɗaya. Wannan magana ba tare da jayayya ba, daidaituwa ko a'a?

Ba a bayar da bayanin lambobi biyu masu zuwa ba. Su ne 496 da 8128. An gano lambobi huɗu na farko a farkon karni na XNUMX AD ta hanyar Nicomachus na Gerasa, masanin falsafa kuma masanin lissafi wanda ya rayu a tsohon birnin Dekapolis, yanzu Jordan, wanda yake na Daular Roma.

Domin samun cikakkiyar lamba ta biyar dole ne mu yi babban tsalle a cikin tarihi har sai mun kai karni na sha biyar, tun da cikakkiyar lamba ta biyar 33 550 336 ta bayyana a rubuce-rubuce daga wannan karni. Na shida da na bakwai, 8.589.869.056 da 137.438.691.328, an gano su ne bayan karni guda, a cikin 1588, masanin lissafin Italiyanci Pietro Cataldi.

Kamar cikakkun lambobi, iyakataccen adadin lambobin Mersenne ne kawai aka sani. Sunan lambobin bayan Marin Mason, mutumin da ya fallasa jerin hasashe game da su. Mason masanin Falsafa ne, masanin lissafi, kuma firist (1588-1648).

Euler ne ya gano wadannan lambobi na musamman, godiya ga kafuwar da Mason ya kafa. Leonhard Paul Euler (1707-1783) masanin lissafin Switzerland ne kuma masanin kimiyyar lissafi. Tabbas, sunansa zai riga ya san ku, domin gano cikakken lamba na takwas ba shine kawai nasararsa ba. Hakanan an samo sunanta daga lambar Euler (e), wanda aka yi amfani da shi a yawancin tsarin jiki da na lissafi.

Ina fatan da wannan bayanin zaku iya ƙarin koyo game da waɗannan lambobi da halayensu.


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