20130205, 19:48  #1  
"Bob Silverman"
Nov 2003
North of Boston
2^{2}×1,877 Posts 
Yes, Virginia, there _is_ a largest prime number!
Quote:
I know a larger one. 

20130205, 19:50  #2 
"Bob Silverman"
Nov 2003
North of Boston
2^{2}×1,877 Posts 

20130205, 19:56  #3 
∂^{2}ω=0
Sep 2002
República de California
5·2,351 Posts 

20130205, 19:58  #4  
Aug 2010
Kansas
547 Posts 
Quote:
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) 

20130205, 20:06  #5 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3×29×83 Posts 

20130205, 20:07  #6  
∂^{2}ω=0
Sep 2002
República de California
26753_{8} Posts 
Quote:
But I'm easy. 

20130205, 20:38  #7  
"Bob Silverman"
Nov 2003
North of Boston
2^{2}×1,877 Posts 
Quote:
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. Nonmathematicians 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. 

20130205, 20:44  #8 
If I May
"Chris Halsall"
Sep 2002
Barbados
2B4F_{16} Posts 

20130205, 20:49  #9 
"Bob Silverman"
Nov 2003
North of Boston
2^{2}×1,877 Posts 
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'. 
20130205, 20:58  #10 
If I May
"Chris Halsall"
Sep 2002
Barbados
11,087 Posts 

20130205, 21:26  #11  
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
1110000110101_{2} Posts 
Quote:
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 asyetuntrained senses). Last fiddled with by Dubslow on 20130205 at 21:31 Reason: exclude r=0 

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