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Interesting Numbers- I. Largest Prime Numbers

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 (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 increases upto infinity & mathematicians are trying to find the larger one than the largest, because primes numbers/integers are not symmetrical (as any one cannot guess the next prime after one.) As of now the biggest prime number found is (probably) M-47 , called as Mersenne 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.

Image via RepulicOfMath.WordPress.com

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