Question

do anyone know what is the largest prime number?

Answer 1

id guess its infinity, but thats most likely wrong an some account

Answer 2

2^43,112,609 − 1

it has 12,978,189 digits

Answer 3

there is no largest prime. if there was one, then you could always find a larger one by multiplying all the ones you have found so far and then subtracting one from the result.
e.g. lets say you thought the only primes were: 2, 3, 5
then 2*3*5=30
take one away gives 29 which is now a new prime.

Answer 4

There is the largest known prime number--which will be out on the web somewhere--and then there is the largest prime number altogether.

The fact is, however, is there is no such thing as the largest prime number.

Answer 5

the largest known prime number is what i have stated above

Answer 6

its all here http://primes.utm.edu/largest.html

Answer 7

Normally that there is no largest prime goes like this:
Suppose \( p_1, p_2, ..., p_N \) are all the prime numbers. That is, we are arguing by contradiction by starting with the assumption there is a finite number, N, of prime numbers. Our job now is to show this assumption leads to a contradiction.

Consider the number
\[ q = p_1 p_2 p_3 ... p_N + 1 \]

Then q is not divisible by any of the prime numbers \( p_j \) and therefore q itself must be prime. Contradiction. Therefore there are an infinite number of primes.

Answer 8

Normally the proof that there is no largest prime ....

Answer 9

JamesJ (and saruz) are right - I did not give the proof correctly. But basically - there is no largest prime.

Answer 10

what lilg132 gave is the largest known prime..

Answer 11

note that :\[q=p_1p_2\cdots p_N+1\]may or may not be prime. the contradiction you want is that is cant be divisible by any of the N primes you thought were all the primes, so it must be prime or divisible by a another prime not on the list.

Example:
\[2\cdot3\cdot5\cdot7\cdot11\cdot13+1=30031=59\cdot509\]where 59 and 509 are prime.

Answer 12

Yes, I was very sloppy. That's for picking that up.