<prompt> Etsa lipatlisiso me u hlalose hore na thepa ea nomoro ea mantlha ke efe.nan  <response>: Instruction in English: Research and explain what are the properties of a prime number. . Response in English: A prime number is a natural number greater than one that is not a product of two smaller natural numbers. In other words, it is a number that has only two distinct factors: 1 and itself. For example, the first six prime numbers are 2, 3, 5, 7, 11, and 13. Here some important properties of prime numbers:1. Divisibility: A prime number is only divisible by 1 and itself. This property sets prime numbers apart from composite numbers, which have more than two factors.2. Density: The density of prime numbers in the set of natural numbers decreases as numbers get larger, as stated in the Prime Number Theorem. However, there are still infinitely many prime numbers.3. Unpredictability: The distribution of prime numbers among the natural numbers is considered to be unpredictable. However, there are certain patterns that exist, like the Twin prime conjecture, which hypothesizes that there are infinitely many pairs of prime numbers that differ by 2.4. Unique Factorization: Every whole number greater than 1 can be expressed as a product of prime numbers in exactly one way disregarding the rearrangement of the factors. This property is called the fundamental theorem of arithmetic.5. Importance in Cryptography: Prime numbers are used in various encryption algorithms due to their properties, especially the difficulty of factoring large prime numbers. 6. Goldbachs Conjecture: Goldbachs Conjecture is one of the oldest and best-known unsolved problems in number theory and mathematics in general. It states that every even integer greater than 2 can be expressed as the sum of two prime numbers.These are just some of the many interesting properties and uses of prime numbers, which make them a fascinating area of study in mathematics. . Response in Sesotho: Nomoro e kholo ke palo ea tlhaho e kholo ho feta e le ngoe e sa hlahisoang ke linomoro tse peli tse nyenyane tsa tlhaho. Ka mantsoe a mang, ke palo e nang le lintlha tse peli feela tse fapaneng: 1 le eona. Mohlala, linomoro tsa mantlha tse tšeletseng tsa pele ke 2, 3, 5, 7, 11, le 13. Mona lintlha tse ling tsa bohlokoa tsa lipalo-palo: 1. Karohano: Nomoro e ka sehloohong e aroloa feela ka 1 le ka boyona. Thepa ena e beha linomoro tsa mantlha ho fapana le linomoro tse kopaneng, tse nang le lintlha tse fetang tse peli. 2. Density: The density of prime numbers sete ea linomoro tsa tlhaho e fokotseha ha lipalo li ntse li hola, joalo ka ha ho boletsoe ho Prime Number Theorem. Leha ho le joalo, ho ntse ho e-na le lipalo tse ngata tse ka sehloohong. 3. Ho se tsejoe esale pele: Kabo ea linomoro tse ka sehloohong hara lipalo tsa tlhaho ho nkoa e le ntho e sa lebelloang. Leha ho le joalo, ho na le mekhoa e itseng e teng, joalo ka khopolo-taba ea Twin prime, e hakanyang hore ho na le lipara tse ngata ka ho sa feleng tsa linomoro tse ka sehloohong tse fapaneng ka 2. lipalo ka tsela e le ngoe e sa tsotelleng ho hlophisoa bocha ha lintlha. Thepa ena e bitsoa theorem ea motheo ea arithmetic. 5. Bohlokoa ho Cryptography: Linomoro tse ka sehloohong li sebelisoa mefuteng e fapaneng ea li-encryption algorithms ka lebaka la thepa ea bona, haholo-holo bothata ba ho etsa lipalo tse kholo tsa bohlokoa. 6. Khopolo ea Goldbach: Khopolo ea Goldbach ke e ngoe ea mathata a khale ka ho fetisisa le a tsejoang ka ho fetisisa a sa rarolloang ka khopolo ea lipalo le lipalo ka kakaretso. E bolela hore palo e ngoe le e ngoe e kholo ho feta 2 e ka hlalosoa e le kakaretso ea linomoro tse peli tse ka sehloohong. Tsena ke tse ling tsa lintho tse ngata tse khahlang le tsebeliso ea linomoro tsa mantlha, tse li etsang sebaka se khahlang sa thuto ea lipalo. 