Sieve of Eratosthenes
Eratosthenes, a Greek mathematician, gave a simple method
of finding prime and composite numbers. This method is known as the Sieve of
Eratosthenes.
Using the method of Sieve of
Eratosthenes, we can find the prime numbers and the composite numbers between 0
and any number.
In this article, we will learn how to
find the prime numbers and the composite numbers between 0 and 100. Using this
method, we can also find the prime numbers and composite numbers between 100
and 200, between 200 and 300, between 300 and 400, or between 400 and 500.
How to Find Prime Numbers between 1 and 100?
1. Write numbers up to 100 except 1 which is
neither prime nor composite.
2. Encircle 2 and cross out all other multiples
of 2.
3. Encircle 3 and cross out all other multiples
of 3.
4. Encircle 5 and cross out all other multiples of 5.
5. Encircle 7 and cross out all other multiples of 7.
6. Continue this process till every number is either encircled or crossed out.
All the encircled numbers so obtained
are prime numbers.
Thus, the prime numbers less than 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 and 97.
The remaining numbers between 0 and
100 are composite numbers except 1.
1 is neither prime nor composite
number.
It may be observed that there is no
pattern in the occurrence of prime numbers and as such no formula has been
found so far to find prime numbers. Thus, the only way to find whether the
given number is prime or not is to find if it has any factor other than 1 and
itself.
Prime Numbers between 0 and 100
There
are 25 prime numbers lie between 0 and 100, which are as follows:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29,
31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97
Prime Numbers between 100 and 200
There
are 21 prime numbers lie between 100 and 200, which are as follows:
101,
103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181,
191, 193, 197 and 199
Prime Numbers between 200 and 300
There
are 16 prime numbers lie between 200 and 300, which are as follows:
211,
223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283 and 293
Prime Numbers between 300 and 400
There
are 16 prime numbers lie between 300 and 400, which are as follows:
307,
311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389 and 397
Prime Numbers between 400 and 500
There
are 17 prime numbers lie between 300 and 400, which are as follows:
401, 409, 419, 421, 431, 433, 439,
443, 449, 457, 461, 463, 467, 479, 487, 491 and 499
Prime Numbers between 0 and 500
There
are 95 prime numbers lie between 0 and 500, which are as follows:
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, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491 and 499
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