20080701, 22:38  #1 
2·1,091 Posts 
Possible?
Is it possible that there isn't a prime above 10 million digits? Or that there is a point where there are no more primes?

20080701, 23:21  #2  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
4,271 Posts 
Quote:
http://en.wikipedia.org/wiki/Prime_n..._prime_numbers More proofs at http://primes.utm.edu/notes/proofs/infinite/. It is, however, possible that there is a finite number of Mersenne primes (2^p1, what GIMPS searches for), since it hasn't been proven whether or not there are infinite Mersenne primes. 

20080701, 23:23  #3 
Feb 2006
Denmark
346_{8} Posts 
It seems a plausible conjecture that there are infinitely many Mersenne primes, but based on current knowledge it is still possible that there are none above 10 million digits. It is known there are infinitely many nonMersenne primes.

20080702, 04:16  #4 
Jun 2003
5264_{10} Posts 
Much more probable is that there are no 10 million digit mersenne primes that are accessible by current technology (like, say, the region from 10M10G is barren).

20080707, 02:42  #5  
"Lucan"
Dec 2006
England
2·3·13·83 Posts 
Quote:
The chance of this barren patch is 1/1000^2.57 

20080707, 09:54  #6 
"Lucan"
Dec 2006
England
2×3×13×83 Posts 
