20151111, 02:30  #166  
Romulan Interpreter
Jun 2011
Thailand
2^{2}·7·11·29 Posts 
CRG means:
Quote:


20151111, 03:10  #167 
"Rashid Naimi"
Oct 2015
Remote to Here/There
3632_{8} Posts 
There are infinite forms of sums possible, but in your example it seems that you would need to know what p the largest prime is, which is not necessary.
There is a small numeric example in my post 39 of what I mean. It is a small number but the concept applies to any size. There again you need a list of primes which is in fact not necessary. for example you can use the form: p=15!/(7^2) 7^x and solve for x where p < 15^2 which will end up being p<13^2. But you don't need to know that or the fact the largest prime factor is13. That is a very simple example. A more improved form is the number format that i have given for the large primes I have listed, which is basically the sum of a multifactorial and a small primorial and the mutifactorial's number of "!" is equal to the primorial which gurantees coprimeness of the addends. It is no coincidence it yields a lot of primes. In fact try making the 2nd input in my WDP code a few times larger than the 1st and you are likely to run into composites very rarely in multik digits.Optimize the code/sums by some prime powers and converge to less than the square of the largest factor (not prime) and you are guaranteed primality. No other proof needed. 
20151111, 04:02  #168 
"Rashid Naimi"
Oct 2015
Remote to Here/There
11110011010_{2} Posts 
This is probably a better example/description for optimization of a simple example for small numbers:
p=2^y x 15!/(7^2) 7^x and solve for x and y, where p < 15^2 ETA I myself can only solve for a much smaller, 4! of the format: Link Last fiddled with by a1call on 20151111 at 04:40 
20151111, 07:48  #169 
"Frank <^>"
Dec 2004
CDP Janesville
4062_{8} Posts 

20151111, 15:08  #170 
Aug 2006
2·2,969 Posts 
In any case the code you provided is just repeatedly testing numbers until it finds a prime. This doesn't take any special thought to derive, and it can be done much more efficiently by existing programs which sieve much further than your effective sieve.
The number in your sample code, for example, was the 49th that you tested. Last fiddled with by CRGreathouse on 20151111 at 15:11 
20151111, 15:13  #171 
Aug 2006
5938_{10} Posts 
I'll believe it when I see it. The code you posted generated 48 composites before it hit on a prime.

20151111, 16:50  #172  
"Rashid Naimi"
Oct 2015
Remote to Here/There
2·7·139 Posts 
Quote:


20151111, 16:54  #173  
"Rashid Naimi"
Oct 2015
Remote to Here/There
2×7×139 Posts 
Quote:
It does not really make a difference if you believe this or not. 

20151111, 17:07  #174  
"Dana Jacobsen"
Feb 2011
Bangkok, TH
2×3×151 Posts 
Quote:
This is all way too complicated, with too many things floating around (e.g. are we still talking about 1000M digit primes? Is PrimeQ expected to be used? What is theorem 2?). The method being shown, using a PRP test (e.g. PrimeQ) is a terrible distraction. I don't think it's particularly interesting to people. I think a1call (OP) is saying this is related to his theorem 1 method, but not really it. We need to see it properly working then, with a single PrimeQ at the end that asserts "I have failed, something has gone terribly wrong, do not use this code!" if it ever fails. On success we should get the number followed by some sort of container holding everything we need to prove it prime by theorem 1 (post 39, page 4): P_n, b_sign, c_sign, V. Let V be a vector of length n holding the exponents used by b and c, using their sign to denote B vs. C. That should let us reconstruct b and c and verify everything including d < (P_n)^2. This is just an example  some other structure is fine as long as we can recover everything needed to show the result must be prime. I know it isn't theorem 2, and the method isn't efficient enough to be a big deal, but at least it would stop the discussions of probability and probable prime tests. Last fiddled with by danaj on 20151111 at 17:09 

20151111, 17:20  #175  
"Forget I exist"
Jul 2009
Dumbassville
20261_{8} Posts 
Quote:
Last fiddled with by science_man_88 on 20151111 at 17:20 

20151111, 17:34  #176 
Aug 2006
5938_{10} Posts 
Every example you have posted is of the same general form: B + sk with a big number B and a small number s, with B + s, B + 2s, ..., B + (k1)s all composite and B + sk prime. It looks exactly like what it is: a crude form of sieving with lots of primality tests.

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