Yes, Virginia, there _is_ a largest prime number!

R.D. Silverman · 2013-02-05, 19:48

Quote:

Originally Posted by ixfd64

NBC News: http://www.nbcnews.com/id/50707223/n...cience-science

Another "largest prime number" fail.

The recent discovery isn't even the largest KNOWN prime.

I know a larger one.

R.D. Silverman · 2013-02-05, 19:50

Quote:

Originally Posted by R.D. Silverman

The recent discovery isn't even the largest KNOWN prime.

I know a larger one.

Any prime you can name, I can name bigger,
I can name any prime bigger than you.

No you can't.
Yes, I can.
No you can't.
Yes I can, yes I can, yes I can!

ewmayer · 2013-02-05, 19:56

Quote:

Originally Posted by R.D. Silverman

I know a larger one.

Not explicitly, you don't.

This has been covered numerous times before.

c10ck3r · 2013-02-05, 19:58

Quote:

Originally Posted by R.D. Silverman

The recent discovery isn't even the largest KNOWN prime.

I know a larger one.

Doctor Silverman, I for one am dying to know this number. Please send the full decimal representation of this number as a Word document to: mersenneforum@gmail.com
Don't worry if it takes multiple emails, that's fine. Also, send an attachment of the proof to the same address.
Much obliged.
John Shook, PhD
(Patiently hoping for a degree)

Dubslow · 2013-02-05, 20:06

Quote:

Originally Posted by c10ck3r

John Shook, PhD
(Patiently hoping for a degree)

Heh, that's a good one, I'm remembering that for further use

ewmayer · 2013-02-05, 20:07

Quote:

Originally Posted by c10ck3r

Doctor Silverman, I for one am dying to know this number. Please send the full decimal representation of this number as a Word document to: mersenneforum@gmail.com

I'll settle for a photo (and accompanying official press release) of RDS holding up a check from EFF for all the remaining record-prime prizes.

But I'm easy.

R.D. Silverman · 2013-02-05, 20:38

Quote:

Originally Posted by ewmayer

I'll settle for a photo (and accompanying official press release) of RDS holding up a check from EFF for all the remaining record-prime prizes.

But I'm easy.

I did NOT, repeat NOT say that I knew its decimal (or binary) representation.

I can however, give an exact (mathematically precise) specification of a
larger prime. Determining its decimal representation would take a bit of
computing.......

Given any prime, one can always give a larger one.

You knew this, of course. There are lots of numbers for which one can
give a precise representation. But not in decimal.......

I am pointing out something that should be obvious. It is possible to know
a number without knowing its decimal (or binary) representation.
Non-mathematicians often confuse one with the other.

Let M48 be the newly discovered prime.

Ackerman(M48, M48) is a uniquely and precisely defined number. But I
wouldn't want to compute it in decimal.

chalsall · 2013-02-05, 20:44

Quote:

Originally Posted by R.D. Silverman

Ackerman(M48, M48) is a uniquely and precisely defined number. But I wouldn't want to compute it in decimal.

What a waste of carbon....

R.D. Silverman · 2013-02-05, 20:49

Quote:

Originally Posted by ewmayer

Not explicitly, you don't.

Yes, I do. I can give an explicit definition.

In formal automata/language theory it can be specified exactly. (or
as you say, "explicitly"). Of course if one wants to be fuzzy in the definition
of the word "explicit" then it sort of becomes meaningless.

It just depends on the (formal) language one is willing to accept.

If one only accepts decimal (or binary), then one is going to be
very limited in the numbers one can specify. i.e. try specifying 'pi'.

chalsall · 2013-02-05, 20:58

Quote:

Originally Posted by R.D. Silverman

i.e. try specifying 'pi'.

U+03C0.

Dubslow · 2013-02-05, 21:26

Quote:

Originally Posted by R.D. Silverman

Yes, I do. I can give an explicit definition.

In formal automata/language theory it can be specified exactly. (or
as you say, "explicitly"). Of course if one wants to be fuzzy in the definition
of the word "explicit" then it sort of becomes meaningless.

It just depends on the (formal) language one is willing to accept.

If one only accepts decimal (or binary), then one is going to be
very limited in the numbers one can specify. i.e. try specifying 'pi'.

'pi' is the smallest strictly positive solution x of the following equation defined over the reals: $\sum_{i=0}^\infty {\frac{(-1)^i x^{2i+1}}{(2i+1)!}} \quad = \quad 0$ (this happens to be the ratio of the circumference to diameter of a "circle", i.e. the set of points $S^1 = \{(x,y)\in \mathbb{R}^2 | x^2+y^2=r^2,\quad \forall r \in\mathbb{R}\backslash \{0\} \}$ . If you really want to get fancy, the circumference and diameter can be defined by some suitably abstract integral [but I haven't had enough analysis to say much more than that].)

Now, what is your formal specification/explicit definition of a prime larger than M48? Something like Ackerman(M48, M48) is a formally specified number, but I highly doubt its primality (not that you or I could prove it one way or the other). It's quite a bold claim you made (or so it seems to my as-yet-untrained senses).

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