what is a prime number?

Answer 1

A prime number is any number whose only two factors are one and itself. This means that the only whole numbers that divide evenly into a prime number are one and itself. For example, 17. 17 can only be divided evenly by 1 and 17, so 17 is prime (and happens to be my favorite number).

Answer 2

A prime number is a number that can only be divided by itself or the number 1. The prime numbers between 1 to 100 are 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...and they go on forever. So far nobody has found a pattern to predict them. There are debates over whether 1 is considered to be a prime number or not, but generally it is not listed as a prime number.

Answer 3

if this makes sense,your it.

enjoy.
A prime number (or prime integer, often simply called a "prime" for short) is a positive integer that has no positive integer divisors other than 1 and itself. (More concisely, a prime number is a positive integer having exactly one positive divisor other than 1.) For example, the only divisors of 13 are 1 and 13, making 13 a prime number, while the number 24 has divisors 1, 2, 3, 4, 6, 8, 12, and 24 (corresponding to the factorization ), making 24 not a prime number. Positive integers other than 1 which are not prime are called composite numbers.

Prime numbers are therefore numbers that cannot be factored or, more precisely, are numbers whose divisors are trivial and given by exactly 1 and .

The number 1 is a special case which is considered neither prime nor composite (Wells 1986, p. 31). Although the number 1 used to be considered a prime (Goldbach 1742; Lehmer 1909; Lehmer 1914; Hardy and Wright 1979, p. 11; Gardner 1984, pp. 86-87; Sloane and Plouffe 1995, p. 33; Hardy 1999, p. 46), it requires special treatment in so many definitions and applications involving primes greater than or equal to 2 that it is usually placed into a class of its own. A good reason not to call 1 a prime number is that if 1 were prime, then the statement of the fundamental theorem of arithmetic would have to be modified since "in exactly one way" would be false because any . In other words, unique factorization into a product of primes would fail if the primes included 1. A slightly less illuminating but mathematically correct reason is noted by Tietze (1965, p. 2), who states "Why is the number 1 made an exception? This is a problem that schoolboys often argue about, but since it is a question of definition, it is not arguable." As more simply noted by Derbyshire (2004, p. 33), "2 pays its way [as a prime] on balance; 1 doesn't."

With 1 excluded, the smallest prime is therefore 2. However, since 2 is the only even prime (which, ironically, in some sense makes it the "oddest" prime), it is also somewhat special, and the set of all primes excluding 2 is therefore called the "odd primes." Note also that while 2 is considered a prime today, at one time it was not (Tietze 1965, p. 18; Tropfke 1921, p. 96).

The th prime number is commonly denoted , so , , and so on, and may be computed in Mathematica as Prime[n].

The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, ... (Sloane's A000040; Hardy and Wright 1979, p. 3). A mnemonic for remembering the first seven primes is, "In the early morning, astronomers spiritualized nonmathematicians" (G. L. Honaker, Jr., pers. comm., Aug. 4, 2005). In the novel The Curious Incident of the Dog in the Night-Time (Haddon 2003), the protagonist Christopher amusingly numbers the chapters using the prime numbers instead of the (much) more traditional positive integers. In the Season 1 episode "Prime Suspect" (2005) of the television crime drama NUMB3RS, math genius Charlie Eppes realized that character Ethan's daughter has been kidnapped because he is close to solving the Riemann hypothesis, which allegedly would allow the perpetrators to break essentially all internet security by factoring large numbers.

The numbers of decimal digits in for , 1, ... is given by 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, ... (Sloane's A099260).

The set of primes is sometimes denoted , represented in Mathematica as Primes

Answer 4

A prime number (or product) is a number that can only be reached, in terms of multiplication by multiplying any given number by 1. For example, the only way to reach the product of 7 is 7 x 1, or the only way to reach the product of 13 is 13 x 1.
Alternatively, the number 9 can be reached two ways and is therefore NOT a prime number, That is, 9 x 1 (this formula obviously works for all whole numbers), OR 3 x3 .
The sequence begins thus: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41...
The number 2 is the only even prime number as all other even numbers can be reached by multiplying Y (half of the final sum/product) by two, as well as the original number times one,
If there is/are more than one way(s) of reaching any given number via multiplication then it is NOT a prime number.

Answer 5

A prime number is a whole number that can only be divided by itself and 1 to give another whole number.

e.g. 23 is a prime number, because 23/23 = 1, and 23/1 = 23
But 23/3 = 7.66667, 23/9 = 2.55556

25 is not a prime number, because 25/25 = 1 and 25/1 = 25
But 25/5 = 5
5 is another whole number!

Sorry if I've confused you, I'm not very good at explaining things. I hope I've helped, though. :o)

Answer 6

A positive whole number divisible only by itself and one AND has Two different factors...so 1 is NOT a prime number.(dammy0320 & mike s)
2 is the only even prime number:
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47..............................etc

Answer 7

Any number/integer higher than 1 that can only be divided by itself or 1 without leaving a remainder. (I have never understood why poor old 1 is not considered a prime number). Having just read just me's answer I think I nearly understand!

Answer 8

Two is the lesser prime number. The prime must be positive, whole number and divisible without remainder with only one and itself.
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Answer 9

For those claiming 1 is a prime number in their answers; it's not.
1 is considered neither prime nor composite.

Answer 10

A Prime number is a number that can only be divided by 1 and itself. for example 1, 2, 5, 7, 11 e.t.c.