but there is no largest prime number; there are infinitely many

but there is no largest prime number; there are infinitely many

 

Largest known, I suppose.

Posted by fourier jr[/b]

but there is no largest prime number; there are infinitely manyOriginally

 

You can only supose that, but never be sure 100 %

Posted by fourier jr[/b]

but there is no largest prime number; there are infinitely manyOriginally

 

You can only supose that' date=' but never be sure 100 %[/quote']

 

No I suppose NOT and get a contradiction. Haven't you seen any of the proofs?

It's one of the most famous proofs by Euclid, showing that there's an infinite number of primes. It uses the FTA to show that if any number a = p₁p₂...p_n then the number p₁p₂...p_n+1 must be composed of some primes which are not p₁ etc.

 

(At least that's the general jist of it)

Prime numbers are mainly used for encryption. For example, in networking (e.g. Internet) data stream encryption. Large prime number are difficult to be cracked,because calculating them are impractical even for cutting edge CPUs.

As I know, governments will pay lots of money for a large prime number .

By the way, some of the large prime numbers can be copyrighted, which means using them could be illegal...... (<-- I'm not sure how it works)

 

Correct me if I'm wrong~

 

By the way, I just discovered this forum today and it's very helpful~

The record in the original post was beaten recently.

 

Tabling the motion we change the title of the thread to "Larger Prime Number Found", so it's always topical

hmm... just wonder how high it could get. There's got to be a lmit before someone says "I've had it! No more primes for me! Not even for a billionn dollars!"

hmm... just wonder how high it could get. There's got to be a lmit before someone says "I've had it! No more primes for me! Not even for a billionn dollars!"

 

Well I daresay there's enough primes to keep everyone occupied for a very long time

 

(in case anyone misinterprets this statement, it's a joke)

lol! Ok!

It'll get to a point where people will think "this is stupid" at some stage though. Probably when (or if) someone comes up for a formula for the nth prime.

wouldn`t the largest prime be Pi, with or without the decimal point after the 3?

 

 

just a though

It wouldn't necessarily be prime and you'd definately need to take the decimal point away.

 

Plus there's no such thing as "the largest" prime since you can always find a prime bigger than any prime before it (as I mentioned above).

that`s what I thought, and seeing as Pi is infinate, and can only be divided by itself and 1, then by default, as a conscise answer Pi / 10 would be the largest prime

 

or am I being too logical again?

 

[edit] thinking about it `/10` would only shift the decimal point to the left making Pi not a whole number. so maybe Pi X 10^oo would be better, making the decimal point chase the number to the right and still keeping it whole

If that's the case, then

(Pi X 10^oo)(Previous prime number ,P [Pi-1])(P [Pi-2])(P [Pi-3])(P [Pi-4])....(2) + 1

is another prime number (by default)

 

[just realized it's been mentioned above]

Look at it this way; no matter how many times you multiply pi by 10, it can never be a whole number; you can't just multiply things by infinity because it doesn't make logical sense - infinity isn't a number.

Look at it this way; no matter how many times you multiply pi by 10, it can never be a whole number;

 

That's because it is an irrational number which has a decimal but no ending to the decimal, right?

well ok then, by the Function of Pi X 10^(Pi decmal limit), does that work?

there is no decimal limit of pi. Its an irrational number!

if it`s so irrational, then how can it be calculated?

WEll, a round value can be calculated, but, the last digit of the decimal is rounded. It is never an accurate value, even calculators use pi to about 10 decimal places or something. People have got pi to, i think ,about 2 million decimal places, its just never going to end. You can always calculate a rounded value, not an exact one, as it would never end!

agreed, and so by virtue of that, wouldn`t the Function of Pi X 10^(Pi decmal limit) qualify as the largest prime? as a more concise way of explaining it or its determination?

as opposed to a reasonably lengthy algorythm?

 

it was only an idea after all )

Pi decmal limit

 

That's where you're going wrong. There is no decimal limit for pi. Its has an infinite number of deciaml places. Therefore, you would be multiplying it by 10^infinite, which does not exist, like Dave said:

 

Look at it this way; no matter how many times you multiply pi by 10, it can never be a whole number; you can't just multiply things by infinity because it doesn't make logical sense - infinity isn't a number.

But what YT is saying is that if we only know Pi to 3 decimal places (even though there exist an infinite number of them) then taking Pi^(1000) would eliminate all the known decimals and we'd be left with 4 digit whole number. If we know Pi to however-many decimal places (you said 2 million) than you would use only those numbers and mulitply by the apropriate power of ten to eliminate them, thus leaving a whole number. Whether that number will be prime or not, I'm not sure, though. If we only knew Pi to two decimal places we'd have 3.14. Multiply by 10^2 and you get 314, not a prime number. I don't know whether stopping at any point will always yeild a prime, YT, but I hope I explained what you're trying to say right and I hope AOM understands it.

Okay, I don't see the problem here. jordan, what you've said is true but it doesn't prove that pi is the 'largest prime'. As n->infinity, the statement becomes meaningless.