What is a Prime Number?

An integer, say $ p $ , [ $ \ne {0} $ & $ \ne { \pm{1}} $ ] is said to be a prime integer iff its only factors (or divisors) are $ \pm{1} $ & $ \pm{p} $ .

As?

Few easy examples are:
$ \pm{2}, \pm{3}, \pm{5}, \pm{7}, \pm{11}, \pm{13} $ …….etc. This list goes up to infinity & mathematicians are trying to find the larger one than the largest, because primes numbers has no distinct pattern (as any one cannot guess the next prime after one.) As of now the biggest prime number found is  $ M-47 $ , called as Mersenne’s 47. This has an enormous value of $ 2^{43112609} -1 $ . It is very hard to write it on paper because it consists of $ 12978189 $ digits.
»M47 was Invented in 2008.

Other Large Prime Numbers

• The Second Largest prime is $ M-46 $ having value of $ 2^{42643801}-1 $ with $ 12837064 $ digits in it.
»Invented in 2009.

•The Third Largest Prime is $ M-45$ .
»Value:$ 2^{37156667}-1 $
»discovered in 2008 and having $ 11185272 $ digits.

•The Fourth Largest Prime is $ M-44 =2^{32582657}-1$
»digits: $ 9808358$
»discovered in :2006.

•The Fifth largest prime is $ M-43 =2^{30402457}-1$
»digits:$ 9152052$
»discovered:2005

•The Sixth Largest prime is $ M-42$ .
»value:$ 2^{25964951}-1 $
»digits:$ 7816230$
»discovered:2005

•The Seventh Largest prime is $ M-41 $ .
» Value:$ 2^{24036583}$ -1
»digits:$ 7235733$
»discovered:2004

•The Eighth Largest prime is $ M-40 $ .
»Value: $ 2^{20996011}-1 $
»digits:$ 6320430 $
»discovered:2003

•The Ninth Largest prime is $ M-39 $ .
»Value:$ 2^{13466917}-1 $
»digits:$ 4053946 $
»discovered:2001

•The Tenth Largest Known Prime Number is $ M-38 $ .
»Value:$ 19249 times 2^{13018586}+1 $
»digits: $ 3918990 $
»discovered:2007

A Note for Newbie

$ 2^n $ means that $ 2 $ is multiplied with $ 2 $ , $ n $ times. For example: $ 2^5 $ means $ 2 \times 2 \times 2 \times 2 \times 2 = 32 $ .

Prime Numbers and the Year 2011

If we take the 11 consecutive prime numbers from 157 to 211 & sum them up; we get 2011.

Total
0
Shares


Feel free to ask questions, send feedback and even point out mistakes. Great conversations start with just a single word. How to write better comments?
Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

You May Also Like
online books
Read More

Free Online Calculus Text Books

Once I listed books on Algebra and Related Mathematics in this article, Since then I was receiving emails for few more related articles. I have tried to list almost all freely available Calculus texts. Here we go: Elementary Calculus : An approach using infinitesimals by H. J. Keisler Multivariable Calculus by Jim Herod and George Cain Calculus by Gilbert Strang…

Solving Integral Equations (2) – Square Integrable Functions, Norms, Trial Method

Square Integrable function or quadratically integrable function $\mathfrak{L}_2$ function A function $y(x)$ is said to be square integrable or $\mathfrak{L}_2$ function on the interval $(a,b)$ if $$\displaystyle {\int_a^b} {|y(x)|}^2 dx <\infty$$ or $$\displaystyle {\int_a^b} y(x) \bar{y}(x) dx <\infty$$. For further reading, I suggest this Wikipedia page. $y(x)$ is then also called ‘regular function’. The kernel $K(x,t)$ , a function of two variables is…
Screenshot
Read More

Test your counting skills with Branifyd game for Android

Without basic operations of counting, like Addition, Subtraction, Multiplication and Division, it is not possible to imagine math problems. Counting is the base of human life. A student, whether he’s a math major or not, must be good at counting numbers.  The counting ability builds from experience and is definitely a time taking process.   Larger you have given time…
Read More

Solving Ramanujan’s Puzzling Problem

Consider a sequence of functions as follows:- $ f_1 (x) = \sqrt {1+\sqrt {x} } $ $ f_2 (x) = \sqrt{1+ \sqrt {1+2 \sqrt {x} } } $ $ f_3 (x) = \sqrt {1+ \sqrt {1+2 \sqrt {1+3 \sqrt {x} } } } $ ……and so on to $ f_n (x) = \sqrt {1+\sqrt{1+2 \sqrt {1+3 \sqrt {\ldots \sqrt {1+n…

Two Interesting Math Problems

Problem1: Smallest Autobiographical Number: A number with ten digits or less is called autobiographical if its first digit (from the left) indicates the number of zeros it contains,the second digit the number of ones, third digit number of twos and so on. For example: 42101000 is autobiographical. Find, with explanation, the smallest autobiographical number. Solution of Problem 1 Problem 2:…
Read More

The Area of a Disk

If you are aware of elementary facts of geometry, then you might know that the area of a disk with radius $ R$ is $ \pi R^2$ . The radius is actually the measure(length) of a line joining the center of disk and any point on the circumference of the disk or any other circular lamina. Radius for a disk…