20151109, 08:27  #133 
Romulan Interpreter
Jun 2011
Thailand
21344_{8} Posts 
To add into the (futile) 5121 digit stuff, there is a buffer limitation there. Also in pari, if you try to paste the number in pari/gp command prompt window, some digits are ignored, because your copy/paste buffer for command prompt is shorter (limited by windows). Try for example to copy/paste the number without the last 50 digits, "n=<paste>", then copy the last 50 digits and say n=n*10^50+<paste>", then use "Mod(2,n)^(n1)", the fastest way to see if n is 2PRP. Then "Mod(2,1088*n^3+1)^(1088*n^3)".
Alternatively, you can make a separate file, call it "test.gp", put inside Code:
{ n=<your 5121 digit number here, it can be format on many rows, no end character used, use semicolon at the end>; Mod(2,1088*n^3+1)^(1088*n^3) } 
20151109, 13:59  #134  
Nov 2003
2^{6}×113 Posts 
You may have rediscovered two theorems, but they are not yours and claiming that they are
yours constitutes plagiarism. Your theorems are already known. I have given a reference. Quote:
And your assumption is wrong that finding PRP's is the first step in finding large primes. Quote:
You can be enthusiastic. But what you have done so far shows a gross lack of understanding of the algorithms and mathematics behind finding large primes. Your numerical work so far is mindless numerology AND it is trivial when compared against the state of the art. You may be impressed, but no one else is. You are a legend in your own mind. Try reading Crandall & Pomerance's book. Do the exercises. And rather than complain about limitations of the black box applications that you are using to achieve your trivial results, why don't you write your own code? GMP is readily available for the multiprecision arithmetic. You might actually learn something! Quote:


20151109, 14:47  #135  
"Frank <^>"
Dec 2004
CDP Janesville
2·1,049 Posts 
Quote:
Quote:


20151109, 18:34  #136 
"Dana Jacobsen"
Feb 2011
Bangkok, TH
38A_{16} Posts 
There is a lot of pushback, and it's rarely gentle. Especially if the subforum has "Math" in the title, which usually means one is expected to have more rigor and background. This forum in general tends to be more focused toward a different audience than many others  much less beginner level. It's also hurt by starting out wanting to claim the billion digit EFF prize, which immediately sets lots of crank alarm bells ringing. I read some other math forums and they can get quickly overwhelmed by a few people who keep insisting they have rudimentary proofs of Beal's conjecture or FLT, and pretty soon the whole forum becomes useless as it is inundated with daily gibberish. The regulars really don't want that to happen here.
I am assuming you're using the PrimeQ in your function because it isn't your final method. You can't rely on PrimeQ in the long run, or you may as well just run a variant of nextprime. For generating large actual primes, you need to use either a special form that has a very fast proof (e.g. Mersenne) or make sure you have the proof step as you build it. Again a flawed analogy, but given the choice when constructing a semiprime of multiplying two primes vs. factoring composites until we get two prime factors ... it should be obvious which is the better way to do it. 
20151109, 18:46  #137  
Nov 2003
2^{6}·113 Posts 
Quote:
asked about the method used for partitioning his set of primes into two subsets such that the difference between the two products of the primes in each subset satisfied the sqrt condition. There was, of course, no response, which in turn makes one suspicious that the OP does not HAVE a response. 

20151109, 18:47  #138  
Apr 2010
Over the rainbow
100110100110_{2} Posts 
Quote:
just adding a note there : with 5 minutes, with tools already availlable to the public, 3^12311*61, a 5875 digit PRP ( determined as PRP in less than a second), has been proven prime in a second. Special form help a lot to prove primality. And proved the same for 3^18805*61 (8974 digits) in not a lot of more time. (and yeah, I know, those are pointless prime , RDS. It is just to sho the help from special form) Last fiddled with by firejuggler on 20151109 at 19:03 

20151109, 19:54  #139  
"Rashid Naimi"
Oct 2015
Remote to Here/There
7·277 Posts 
Quote:


20151109, 20:00  #140  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
21704_{8} Posts 
Quote:
And why these weird contortions in the number's notation? In general, (AB)!^{(B)} = A! B^{A} because it is simply = {AB}{(A1)B}{(A2)B}...B so why not write it like that? For obfuscation? 

20151109, 20:11  #141 
"Rashid Naimi"
Oct 2015
Remote to Here/There
7·277 Posts 
Thank you schickel, You seem to have a very fast, idle supercomputer. I owe you quite a few CPU clock pulses. I will pay you back if I ever get quantum computer.
But joking aside, there is a at least one layman member on this board which shall remain anonymous. He might not understand the code. For his sake is the 5121 digit integer a prime or a composite? Thank you again for your and your computer's time. 
20151109, 20:15  #142  
"Rashid Naimi"
Oct 2015
Remote to Here/There
7×277 Posts 
Quote:
I was not aware of the buffer limitation. I pasted the 5121 digit integer with a flag 2 in PARI/gp. it does seem messed up. Again I am glad that one of the race car drivers did the run already. 

20151109, 20:28  #143 
If I May
"Chris Halsall"
Sep 2002
Barbados
10010001101010_{2} Posts 
Just going extremely tangential... If you find someone with only 50 posts taking the piss on serious scientists, engineers and/or mathematicians...
Either the newcomer wants to make quick friends (or at least respect)... Or, they slide in and say "Hey guys. Long Time No See". 
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