## Prime number |

A **prime number** (or a **prime**) is a

The property of being prime is called primality. A simple but slow method of checking the primality of a given number , called ^{} the

There are

Several historical questions regarding prime numbers are still unsolved. These include

- definition and examples
- history
- elementary properties
- analytic properties
- abstract algebra
- computational methods
- other applications
- notes
- references
- external links

A *prime number* (or a *prime*) if it is greater than 1 and cannot be written as a product of two natural numbers that are both smaller than it. The numbers greater than 1 that are not prime are called ^{[1]} In other words, is prime if items cannot be divided up into smaller equal-size groups of more than one item,^{[2]} or if it is not possible to arrange dots into a rectangular grid that is more than one dot wide and more than one dot high.^{[3]}
For example, among the numbers 1 through 6, the numbers 2, 3, and 5 are the prime numbers,^{[4]} as there are no other numbers that divide them evenly (without a remainder).
1 is not prime, as it is specifically excluded in the definition. 4 = 2 × 2 and 6 = 2 × 3 are both composite.

The ^{[5]}
Yet another way to express the same thing is that a number is prime if it is greater than one and if none of the numbers divides evenly.^{[6]}

The first 25 prime numbers (all the prime numbers less than 100) are:^{[7]}

2 ,3 ,5 ,7 ,11 ,13 ,17 ,19 ,23 ,29 ,31 ,37 ,41 ,43 ,47 ,53 ,59 ,61 ,67 ,71 ,73 ,79 ,83 ,89 ,97 (sequence A000040 in theOEIS ).

No *odd prime*.^{[8]} Similarly, when written in the usual ^{[9]}

The *P*)^{[10]} or by (a ^{[11]}

Other Languages

Afrikaans: Priemgetal

Alemannisch: Primzahl

Ænglisc: Frumtæl

العربية: عدد أولي

aragonés: Numero primero

অসমীয়া: মৌলিক সংখ্যা

asturianu: Númberu primu

azərbaycanca: Sadə ədəd

বাংলা: মৌলিক সংখ্যা

Bân-lâm-gú: Sò͘-sò͘

беларуская: Просты лік

беларуская (тарашкевіца): Просты лік

български: Просто число

bosanski: Prost broj

brezhoneg: Niver kentael

català: Nombre primer

čeština: Prvočíslo

Cymraeg: Rhif cysefin

dansk: Primtal

Deutsch: Primzahl

eesti: Algarv

Ελληνικά: Πρώτος αριθμός

español: Número primo

Esperanto: Primo

euskara: Zenbaki lehen

فارسی: عدد اول

føroyskt: Primtal

français: Nombre premier

Gaeilge: Uimhir phríomha

galego: Número primo

贛語: 質數

ગુજરાતી: અવિભાજ્ય સંખ્યા

хальмг: Экн тойг

한국어: 소수 (수론)

Hawaiʻi: Helu kumu

հայերեն: Պարզ թիվ

हिन्दी: अभाज्य संख्या

hornjoserbsce: Primowa ličba

hrvatski: Prosti broj

Bahasa Indonesia: Bilangan prima

interlingua: Numero prime

íslenska: Frumtala (stærðfræði)

italiano: Numero primo

עברית: מספר ראשוני

Basa Jawa: Wilangan prima

ಕನ್ನಡ: ಅವಿಭಾಜ್ಯ ಸಂಖ್ಯೆ

ქართული: მარტივი რიცხვი

қазақша: Жай сан

Kiswahili: Namba tasa

Kreyòl ayisyen: Nonm premye

kurdî: Hejmarên hîmî

Кыргызча: Жөнөкөй сан

Latina: Numerus primus

latviešu: Pirmskaitlis

Lëtzebuergesch: Primzuel

lietuvių: Pirminis skaičius

Limburgs: Priemgetaal

la .lojban.: nalfendi kacna'u

lumbaart: Numer primm

magyar: Prímszámok

македонски: Прост број

മലയാളം: അഭാജ്യസംഖ്യ

मराठी: मूळ संख्या

مصرى: عدد اولى

Bahasa Melayu: Nombor perdana

монгол: Анхны тоо

မြန်မာဘာသာ: သုဒ္ဓကိန်း

Nederlands: Priemgetal

日本語: 素数

Nordfriisk: Primtaal

norsk: Primtall

norsk nynorsk: Primtal

occitan: Nombre primièr

ଓଡ଼ିଆ: ମୌଳିକ ସଂଖ୍ୟା

oʻzbekcha/ўзбекча: Tub son

ਪੰਜਾਬੀ: ਅਭਾਜ ਸੰਖਿਆ

پنجابی: پرائم نمبر

Patois: Praim nomba

ភាសាខ្មែរ: ចំនួនបឋម

Piemontèis: Nùmer prim

Plattdüütsch: Primtall

polski: Liczba pierwsza

português: Número primo

română: Număr prim

русский: Простое число

Scots: Prime nummer

shqip: Numri i thjeshtë

sicilianu: Nùmmuru primu

සිංහල: ප්රථමක සංඛ්යා

Simple English: Prime number

slovenčina: Prvočíslo

slovenščina: Praštevilo

ślůnski: Pjyrszo nůmera

Soomaaliga: Tiro mutuxan

کوردی: ژمارەی سەرەتایی

српски / srpski: Прост број

srpskohrvatski / српскохрватски: Prost broj

suomi: Alkuluku

svenska: Primtal

Tagalog: Pangunahing bilang

தமிழ்: பகா எண்

తెలుగు: ప్రధాన సంఖ్య

ไทย: จำนวนเฉพาะ

Türkçe: Asal sayı

українська: Просте число

اردو: مفرد عدد

vèneto: Nùmaro primo

vepsän kel’: Palatoi lugu

Tiếng Việt: Số nguyên tố

Võro: Algarv

walon: Nombe prumî

文言: 質數

West-Vlams: Priemgetal

Winaray: Panguna nga ihap

ייִדיש: פרימצאל

Yorùbá: Nọ́mbà àkọ́kọ́

粵語: 質數

Zazaki: Amaro primal

žemaitėška: Pėrmėnis skaitlios

中文: 素数