finding how many prime numbers there are !

[ronhongxo]

the question : How many prime numbers are there between 20 and 30?

is there a easy way to figure that out , without writing all the numbers out !?
HELP !

 

[stapel]

is there a easy way to figure that out , without writing all the numbers out !?

There are only eleven numbers between twenty and thirty, only five of which are odd (and thus potentially prime).

What is the difficulty with checking a mere five small numbers...?

Eliz.

 

[Denis]

We Canadians are too busy making hockey pucks, Stapel :idea:

 

[ronhongxo]

yeahh..but what if the question was
'how many prime numbers are there between 1 and 2000 !?'
:?: :!: :?: :!:

 

[Denis]

Primes >10 must end with 1,3,7 or 9;
since not all of those are primes, then
number primes below 2000 < 4/10 * 2000;
that's all you can do.
There's actually 303.

 

[stapel]

what if the question was 'how many prime numbers are there between 1 and 2000?'

Then different techniques might come into play, and the exercise would take longer. Fortunately, you were asked a much, much simpler question.

Eliz.

 

[galactus]

How many numbers between 20 and 30 are prime?. My goodness, you should be able to see that, effortlessly. A prime is a number which is only divisible by itself and 1. Which numbers between 20 and 30 fit that criterion?.

Is 20 divisible by something else besides itself and 1?. How about 23?. How about 27?.

 

[pka]

A prime is a number which is only divisible by itself and 1.

Using that definition makes 1 a prime number.
How about: a prime number is a positive integer with exactly two divisors.

 

[galactus]

Touche', pka.

 

[jwpaine]

EDIT: without writing all the numbers out? Just use an iteration, comparing each number in your set to all proceeding integers...are any divisible?. This is where computers can help us... or do it on your calc.




we can find this by hand, using the Sieve of Eratosthenes: a simple approach often taught in algebra 1.

a prime is a number only divisible by itself and 1.

make a table of numbers from 1 to x

lets start with a small set of number from 1 to 10

1 2 3 4 5 6 7 8 9 10

you can start by erasing 1.

2 is our first prime, so go ahead and circle 2. now cross out every multiple of 2. so 4 6 and 8 get deleted.

we are left with:

2 3 5 7 9

we are on number 3 now. Circle 3, then continue to cross out all multiples of 3. this would delete 9.

now we have 2 3 5 7

there are no multiples of 5 or 7 in our list. so we can conclude that the primes between 2 and 10, are {2,3,5,7}