20040317, 14:42  #12 
Dec 2003
Hopefully Near M48
2×3×293 Posts 
So the LL test does not win the "race to infinity" for finding ever larger primes (compared to other methods)?

20040317, 16:05  #13  
P90 years forever!
Aug 2002
Yeehaw, FL
2·3,371 Posts 
Quote:
1) search for a 1 to 1.5 billion digit Mersenne prime. If none found: 2) start searching for billion digit generalized fermats too. 3) If you get to 4 billion digit Mersenne numbers and 2.6 billion digit generalized fermat numbers and still haven't found a prime, then start searching for billion digit Proth primes too. 

20040317, 22:12  #14 
Mar 2004
381_{10} Posts 
So if there are no Mersenne Primes with less than 1.5 billiion digits, it is the best thing to search for generalized fermat primes, becasue there are pleny of them. you can just square the basis and half the exponent, and the searching field gets much bigger.
If we estimate about 1000 cpu years on a average P4 for a single test, and a chance of 1 in 300Million I doubt that it is worth the electricity just for the price. But the fascination in that is somewhere else. 
20040318, 17:59  #15  
"Richard B. Woods"
Aug 2002
Wisconsin USA
7692_{10} Posts 
Quote:
No, the LL test always wins, compared to other methods, for samesized numbers. But there are only three or four Mersenne numbers (not to mention that most have composite exponents) in any given range denoted by a certain number of decimal digits, whereas there are millions and millions of exactly1,000,000,000digit nonMersenne primes waiting to be discovered by methods other than LL. Then, as one extends LL testing to Mersenne numbers of more than 1,000,000,000 digits, the time required gets longer, and eventually exceeds the time required for a nonLL test of a 1,000,000,000digit nonMersenne number. After one factors in the differing predicted densities of primes, one finds a tradeoff point at which it's more costeffective to switch to an asymptotically slower method on smaller numbers. 

20040320, 11:35  #16 
Dec 2003
Hopefully Near M48
2·3·293 Posts 
So if I ask for a prime with at least n digits in as small a time as possible, which method should I use as n approaches infinity?

20040320, 18:11  #17  
"William"
May 2003
New Haven
2×3^{2}×131 Posts 
Quote:
William 

20040320, 22:33  #18  
Jun 2003
The Computer
2^{2}·5·19 Posts 
Quote:
LLs would take 852 years, 209 days, 1 hours, 27 minutes for that exponent! 

20040321, 00:40  #19  
"William"
May 2003
New Haven
2×3^{2}×131 Posts 
Quote:
Will Prime95 AdvancedFactor work this large? It didn't work my machine. I think Luigi was using his own program. I was using Excel with the Zmath addin. William 

20040321, 19:30  #20  
Banned
"Luigi"
Aug 2002
Team Italia
4,751 Posts 
Quote:
Luigi 

20040321, 21:22  #21  
"William"
May 2003
New Haven
4466_{8} Posts 
Quote:
Quote:
In the spreadsheet, I noticed that occasionally the value of mod(2^p, 2kp+1) was a power of 2, and this leads to other Mersenne factors. You might want to consider checking for these possibilities and saving the results for later processing. 

20040322, 00:06  #22 
Jun 2003
The Computer
2^{2}·5·19 Posts 
Can you modify Prime95 source code? Perhaps it could be 23.9.

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