Prime Number :
Prime Number is a positive number ( >0 ) that is divisible only by 1 and itself.
Example 1:
We will consider the number 5.
The Number 5 is exactly divisible only by 1 and 5 (itself).
No other numbers less than 5 (2,3,4) can divide 5. SO 5 is a perfect prime number.
Example 2:
We will consider the number 6.
The Number 6 is exactly divisible only by 2 and 3, other than 1 and 6.
SO 6 is a not a prime number.
Large Prime Number can be calculated by the following method :
Method:
This method can be used to calculate primes larger then 100.
Procedure:
a) Calculate the whole number (w) greater then square root of n.
b) Find the prime numbers[p(x)] less than the whole number(w).
c) Now check if the given number n is divisible by any of the prime numbers p(x).
d) If it gets divided then the number n is not a prime number else it is a perfect prime number.
Example:
Validate if 131 is prime number.
Step1:
Square root of 131 = 11.44
So rounding it to the nearest large whole number it becomes 12.
Step2:
Prime Numbers less than 12 are 2,3,5,7,11
Step3:
Given number 131 is not divisible by 2 or 3 or 5 or 7 or 11
So the given number is a prime perfect number.
Interesting Information:
Initially it was assumed that the prime numbers are randomly distributed. In a 1975 lecture, D. Zagier commented "There are two facts about the distribution of prime numbers of which I hope to convince you so overwhelmingly that they will be permanently engraved in your hearts. The first is that, despite their simple definition and role as the building blocks of the natural numbers, the prime numbers grow like weeds among the natural numbers, seeming to obey no other law than that of chance, and nobody can predict where the next one will sprout.
The second fact is even more astonishing, for it states just the opposite: that the prime numbers exhibit stunning regularity, that there are laws governing their behavior, and that they obey these laws with almost military precision".
Later with primes number counting an interesting fact was reveled ( Sloane's ).
Perfect Prime number counting is nothing but the total count of prime numbers up to the given number.
Example:
Prime number count of 2 = 1 (2)
Prime number count of 3 = 2 (2,3)
Prime number count of 4 = 2 (2,3)
Prime number count of 5 = 3 (2,3,5)
So here we can see a regularity,
The first few values of primes are n = 1, 2, 3, 5, 7, 11, 13...
The prime count of primes are ||(n) = 0, 1, 2, 2, 3, 3, 4, 4... (Sloane's).
|
|
