Prime Numbers

The set is well defined. Whether or not a given integer belongs to the set of prime numbers is clearly defined even if, for extremely large numbers, it may prove impossible to determine the status of that number.

'23' .29'

All ther rest are composite.

2 x 11 = 22

2 x 12 = 24

5 x 5 = 25

2 x 13 = 26

3 x 9 = 27

4 x 7 = 28

5 x 6 = 30

There are 11 nines in the numbers from 1 to 100: 9, 19, 29, 39, 49, 59, 69, 79, 89, and 99.

A composite number has a unique prime factorization, but there can be different factor trees that lead to it depending on what factors you choose.

36

18,2

9,2,2

3,3,2,2

36

6,6

2,3,6

2,3,2,3

36

9,4

3,3,4

3,3,2,2

36

12,3

3,4,3

3,2,2,3

The number 1,000,000,000,000,000,000,000,000 can be expressed in numbers as 1 followed by 24 zeros. This is also known as 1 septillion in the short scale naming system. In scientific notation, this number would be written as 1 x 10^24.

89 and 91 are both prime numbers, so when asked the prime number closest to 90, the answer is that 90 is surrounded by two prime numbers

The prime factorization of 120 is not 2345 because 2345 is not a factor of 120. The prime factorization of 120 is 2^3 * 3 * 5, which means that 120 can be expressed as the product of primes 2, 3, and 5.

Because all larger numbers that end in '5' or '0' are divisible by '5'. Hence they are compound numbers.

e.g.

50/5 = 10

1,000,000/ 5 = 200,000

All numbers have factors. Some numbers have some of the same factors as other numbers. These are common factors. If the factor is a prime number, it is a common prime factor.

3 is a prime number.

3 is a factor of 9.

3 is a factor of 12.

3 is a common prime factor of 9 and 12.

Any number that ends with the digit 5 is divisible by 5.

Any number that ends with the digit 5 is divisible by 5.

Any number that ends with the digit 5 is divisible by 5.

Any number that ends with the digit 5 is divisible by 5.

5, all other numbers ending in 5 are divisible by 5.

Any number however, large or small that ends in '5' or '0' is divisible by five.

e.g. 50 / 5 = 1-

1,000,005 / 5 = 200,001

.43. is Prime

44 is composite ( 2 x 22)

45 is composite ( 3 x 15)

To find a prime number.

#1. If an even number (ending in 0,2,4,6,8,) it is NOT a prime number. It is a composite with a factor of '2'

#2. An ODD Number ending in '5' is NOT a prime number., It is a composite of '5'

#3. If the digits of an ODD number sum to '9' , then it is NOT a prime number, It is a composite of '9'

#4. To test for a prime number, divide by '3' & '7' , if there is a remainder to either division it is a prime number. The answer MUST NOT be a whole number. Then it is possible prime number.

e.g.

839

#1. NOt EVEN

#2 . Does NOT end in '5'

#3. The digits sum to 8+3+9 = 20 (Does not divide by ;9;)

#4. 839/3 = 279 remainder '2' or 839/7 = 119 remainder '6' So 839 is a prime number.

As it is an EVEN Number .

All EVEN Numbers are divisible by '2' . Hencethey are composite, and NOT Prime numbers.

NB Any number ending in 0,2,4,6,8 is an EVEN Number, and there fore NOT a prime , except for '2' itself.

e.g. 1,000,000 ( One million is an even number m because it ends in '0' , and is therefore not a prime.

NNB Any number ending in 1,3,5,7,9 is ODD. However, NOT all ODD Numbers are prime numbers. Any number ending in '5' is NOT a prime number, except '5' itself, because they are all divisible by '5', hence composite.

e.g. 1,000,005 (One million and five) is NOT a prime, n]because it ends in ;5;.

NNNB Any number where they digits sum to '9' is NOT a prime number. Because they number is divisible by '9'

e.g. 153 ; 1+ 5 + 3 = 9 . So 153 / 9 = 17 -

NNNNB

To test for a prime divide by either '3' or '7' If the answer has NO remainder, then it is NOT a prime number. If there is a remainder, then it is a prime number.

e.g. 839 /3 = 279 remainder '2' So possible prime

839 / 7 = 111 remainder '8' So '839' is a prime number.

The highest prime number after '11' is infinitely high!!! To the point no one knows it!!!!!

However, I think you mean ' The next higher prime number after '11'? , Which is '13'.

All of the numbers that end in 5 are multiples of 5 which means that they have more than two factors.

63,64,65 aare NOT prime number.

63 = 9 x 7

64 = 8 x 8

65 =5 x 13

They are all composite numbers.

1001

54 = 47 + 7

84 = 79 + 5

NB 5,7,47,79 are all prime numbers.

Let the unkniwn number be 'x'

Hence

54 + x = 112

Subtract '54' from both sides.

54 - 54 + x = 112 - 54

x = 112 - 54

x = 58 The answer!!!!!

'47' is a prime number.!!!

So you can only use

1,47

NO!!!!

Reason , all even numbers will divide by '2'. Hence they are compound numbers, and NOT PRIME numbers.

NO!!!!

588 is an EVEN number, so it will divide by '2', making it a compound number.

Remember

numbers ending in 0,2,4,6,8 are even numbers. They divide by '2' making them compound numbers, hence NOT prime numbers.

ODD numbers ending in 1,3,7,9 may be prime numbers. NB Number ending in '5' are compound number , because they will divide by ;5;.