Home » Math » Interesting Numbers- I. Largest Prime Numbers

# 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