20140926, 03:00  #1 
Jun 2003
1,579 Posts 
Calcprimes program
I have been using the calcprimes.jar program I found on the forum to calculate the odds of finding primes. Overall I have found it very accurate. Are there any sequences that anyone knows of that beats the odds predicted by the program?
Do all the Riesel k<300 follow the odds predicted by the program? Looking at the statistics of the various drives the program looks accurate. 
20140927, 14:07  #2 
Dec 2011
After milion nines:)
5×281 Posts 
Hi!
I just search for that program and in "my range" show 1.79 expected primes. I should hope that will be 2 primes :)) Thanks for program, and if it is accurate as you say, that is good news for me :) Quick sieve test ( on known set of primes) REPORTED PREDICTED 2*10^n1 28 23.84 3*10^n1 19 20.45 5*10^n1 25 24.74 6*10^n1 31 27.63 8*10^n1 23 23.42 9*10^n1 20 18.05 so it looks pretty accurate to me :) Last fiddled with by pepi37 on 20140927 at 14:38 Reason: add more info 
20140927, 16:25  #3 
"Curtis"
Feb 2005
Riverside, CA
2·5·467 Posts 
Citrix
A sequence that "beats the odds" is a matter of statistical distribution there are surely a few that substantially beat the estimate so far, but we have no reason to think they will continue to do so. Like rolling dice, past performance is not connected to future results. If you are asking if any sequence exceeds the odds and we have a reason to think it will continue to do so, that 'reason' would be publicationworthy in most cases. So, no. Pepi The theory that program uses is wellknown, and any inaccuracies are due to the irregular nature of the distribution of primes rather than any error/inaccuracy in the program. 
20140927, 17:04  #4 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·4,663 Posts 
I would expect those forms that have a partial algebraic factorization to need a correction coefficient (f < 1, not in the direction of 'beating the odds'). Consider 27*2^n1.

20140927, 21:40  #5  
Jun 2003
11000101011_{2} Posts 
Quote:
The likelihood increases in the case of mersenne numbers/GM/GQ as the size of the p increases by a factor of ln(p). It would remain constant for a Generalized fermat series depending on the exponent. The increased likelihood for generalized fermat numbers would be ln(2^x) (where 2^x is the exponent). Is there any way of confirming this empirically. I do not have access to the mersenne factor database/generalized fermat search database to test this. Can anyone disprove this or give a counterexample to this? 

20140927, 21:52  #6 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17×251 Posts 
If you've eliminated those candidates from the sieve file already, I'd expect that the program is still accurate.

20140927, 22:47  #7  
"Curtis"
Feb 2005
Riverside, CA
4670_{10} Posts 
Quote:


20140928, 01:20  #8  
Jun 2003
1,579 Posts 
Quote:
Odds of a regular number being prime= 1/ln(N) Odds of a mersenne being prime (where only prime exponents are used)= [1+ln(p)]/ln(2^p1) For a 50M number this would be 18/50,000,000 ~ 1 in 3 million prime exponents or close to 1 prime in a 50 million n range > which seems about right. I agree that there is not enough data to prove or disprove this. Odds for a GFN number being prime=[1+ln(2^x)]/ln(b^2^x) 

20140928, 07:49  #9 
"Curtis"
Feb 2005
Riverside, CA
2×5×467 Posts 
I think your observation is an obfuscated rephrasing of the structure of the factors of mersenne numbers, while not altering the odds any mersenne trial factored to n bits is prime using the formula applied by calcprimes.
Since mersenne factors are bigger than 2p, you can apply the "odds of prime" as if trial factoring has been done to 2p, which would increase the probability produced by the formula. However, it doesn't mean mersennes are any easier to find per primality test; it merely alters the prefactoring effort/effectiveness. 
20150626, 17:03  #10 
Dec 2011
After milion nines:)
5×281 Posts 
Does same size of sieve(in MB) ( same base, but different K) suggested same number of primes in same range?
Why I asking this: I made test sieves until 1000000 for K 8 sieve size is 1.906 MB, and for K 96 is 1.907 MB When using calcprimes. jar , I got predicted number of 27 primes for K=8 and only 21 primes for K=96 
20150626, 18:50  #11  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17·251 Posts 
Quote:


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