what is prime number?

Answer 1

A number >1 which cannot be factored as the product of two smaller numbers.

EDIT: Some of the answers here incorrectly include 1 as a prime number; it is not prime.

Answer 2

A prime number is a number which is divisible only by 1 and itself.
Example:
2 - divisible only by 1 and 2(itself)
3 - divisible only by 1 and 3(itself)
5 - divisible only by 1 and 5(itself)

1 is neither prime nor composite.

A composite number is a number which can be divided by a number which is not 1 or the number itself.
Example of composite numbers:
4 - divisible by 2(not 1 or 4)
6 - divisible by 2, 3(not 1 or 6)
8 - divisible by 2, 4(not 1 or 8)

i hope that u r clear about prime numbers now.
Thankyou.

Answer 3

A natural number greater than 1 that has no divisor between 1 and itself is said to be prime, hence called a prime number or simply a prime. Every natural number greater than 1 has at least the two distinct divisors 1 and itself; a prime has no others.

The number 2 is a prime, there being no candidate divisors between 1 and itself; from it, all even numbers thereafter are non-prime, i.e. 50% of all subsequent numbers. The numbers 3, 5, and 7 are all prime, meaning that, of the first six such subsequent numbers, precisely half are prime, half non-prime. However, of any subsequent six consecutive numbers, at least one of the odd values must be divisible by 3; including the three even numbers this means that at least 66% must be non-prime. So the trend goes; as we look further afield, with an accumulating collection of primes to be divisors, the density of primes declines progressively. But, no matter how far up the numbers we travel, we never exhaust the primes, nor is there any known point above which all further primes are spaced by more than the minimal value of 2 (representing consecutive odd numbers).

The number of primes is infinite. This is easily proved by postulating otherwise, namely that there is a finite set of primes, then constructing the integer that is 1 greater than the product of all of them. Clearly it is not divisible by any of the postulated ones, since every such candidate leaves a remainder of 1. Hence our constructed integer must be either a new prime or be the product of two integers both not divisible by our postulated primes, pointing ultimately to at least one prime excluded from our postulated set. Clearly, then, the number of primes must thus be unlimited, as must the size of them.

For any natural number N, the number of primes not greater than it is of the order of the logarithm of N. It can be proved also that for any prime p, the next prime is less than 2p. There is no consistency, however; for instance, the nearby numbers 86 629 and 86 677 are both primes, and the virtually adjacent numbers 8 004 119 and 8 004 121 are both primes, called ‘paired primes’. Primes appear to be distributed generally without pattern, but the Mersenne primes provide something of a patterned subset. These develop the fact that 3 = 22 - 1, 7 = 23 - 1, 31 = 25 - 1, and 127 = 27 - 1 to suggest that 2n - 1 is a prime if n is a prime. But the prime n = 11 fails, as do many others. However, the formula holds true for an extended if not unlimited range, for four three-figure primes, for eight four-figure primes, and at least to n = 216 091 (giving a Mersenne prime with over 65 000 decimal digits); it provides one relatively economical means for the esoteric exercise of seeking ever larger prime numbers.

Huge prime numbers have acquired significant utility in the modern world, as keys to encryption.

In mathematics, a prime number (or a prime) is a natural number that has exactly two (distinct) natural number divisors, which are 1 and the prime number itself. An infinitude of prime numbers exists, as demonstrated by Euclid in about 300 B.C.. The first 30 prime numbers 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, 101, 103, 107, 109, 113

The property of being a prime is called primality, and the word prime is also used as an adjective. Since 2 is the only even prime number, the term odd prime refers to all prime numbers greater than 2.

Answer 4

A number which is not divisible by any number other than itself and 1. 1 is not considered a prime.

Answer 5

Hey there!

A prime number is any number that is divisible by 1 or by itself.

Here's an example.

19 has 2 factors, 1 and 19.

Since 19 is divisible by 1 and 19 is divisible by 19, 19 is prime.

Note that 2 is the only even prime integer, since the only factors of 2 are 1 and 2.

Hope it helps!

Answer 6

it is a number divisible by itself and 1. All prime numbers are odd except 2.Note that 1 is not a prime number.

Answer 7

A prime number is a number that can only be divisible by itself and 1.

Answer 8

A prime number is a number whose only (positive) factors are 1 and itself.

For example, 2, 3, and 13 are prime numbers, because:
2's factors are 1 and 2.
3's factors are 1 and 3.
13's factors are 1 and 13.

These numbers are NOT prime (they are composite): 8, 9, 20.

8's factors are 1, 2, 4, 8
9's factors are 1, 3, 9
20's factors are 1, 2, 4, 5, 10, 20

The number 1 is considered neither prime nor composite.

Answer 9

A prime number is a number whose only (positive) factors are 1 and itself.

For example, 2, 3, and 13 are prime numbers, because:
2's factors are 1 and 2.
3's factors are 1 and 3.
13's factors are 1 and 13.

These numbers are NOT prime (they are composite): 8, 9, 20.

8's factors are 1, 2, 4, 8
9's factors are 1, 3, 9
20's factors are 1, 2, 4, 5, 10, 20

The number 1 is considered neither prime nor composite.

Answer 10

A number, other than 1, which is divisible only by 1 and itself.

2, 3, 5, 7, 11, 13, 17, 19, 23, ...