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Old 2008-07-01, 22:38   #1
Xfield$$
 

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Default 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?
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Old 2008-07-01, 23:21   #2
Mini-Geek
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"Tim Sorbera"
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Quote:
Originally Posted by Xfield$$ View Post
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?
No.
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^p-1, what GIMPS searches for), since it hasn't been proven whether or not there are infinite Mersenne primes.
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Old 2008-07-01, 23:23   #3
Jens K Andersen
 
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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 non-Mersenne primes.
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Old 2008-07-02, 04:16   #4
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Originally Posted by Jens K Andersen View Post
but based on current knowledge it is still possible that there are none above 10 million digits.
Much more probable is that there are no 10 million digit mersenne primes that are accessible by current technology (like, say, the region from 10M-10G is barren).
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Old 2008-07-07, 02:42   #5
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Quote:
Originally Posted by axn1 View Post
Much more probable is that there are no 10 million digit mersenne primes that are accessible by current technology (like, say, the region from 10M-10G is barren).
Aha. A chance to use "my" formula based on Wagstaff heuristics.

The chance of this barren patch is 1/1000^2.57
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Old 2008-07-07, 09:54   #6
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Quote:
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The chance of this barren patch is 1/1000^2.57
Note that if we summarize GIMPS testing to date as having
tested all exponents up to 40M, this probability is increased
by a significant factor to (40/33219)^2.57.
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