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 (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.

Gaurav Tiwari

A designer by profession, a mathematician by education but a Blogger by hobby. With an experience of over seven years with WordPress, PHP and CSS3, Gaurav is capable of doing almost anything related to these. Beyond that, He is a mathematics graduate & a civil service aspirant.

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1 Response

  1. January 21, 2016

    […] A list of other ‘large’ prime numbers is available in one of our earlier posts. […]

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