The "one billion minus 999,994,000" digits prime number

[LaurV]

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)^(n-1)", the fastest way to see if n is 2-PRP. Then "Mod(2,1088*n^3+1)^(1088*n^3)".

Alternatively, you can make a separate file, call it "test.gp", put inside

{ 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)
}

Wait...

[R.D. Silverman]

Originally Posted by a1call

I have 2 Theorems

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.

I am not a race car driver and am not claiming to be one. I do think however that the approaches based on my Therems 1 & 2 are valuable in at least finding probable primes which I assume is the 1st step in finding primes.

You do not know enough mathematics to claim whether they are valuable. Stop making grandiose claims.
And your assumption is wrong that finding PRP's is the first step in finding large primes.

I am pleasantly impressed by the amount of probable primes my routine comes up with, but no one is forced to share my enthusiasm.

Again, it is not "YOUR ROUTINE".
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 multi-precision arithmetic. You might
actually learn something!

ETA [/B]Ithink that it is clear that the probable primes that I posted in posts 114 and 115 were independently (from each other) generated. If not, they were generated by adjusting 2 very small (less than 2000) variables in a single routine.

So WHAT??? Why do you imagine that this matters???

[schickel]

Originally Posted by a1call

A few more probable primes for today. All of them have evaluated true for the Wolfram PrimeQ command:

A 3985 digit probable prime:

17540276.........................74041

Originally Posted by a1call

Sorry for the multiple replies but the forum software limited the length of last reply.

A 5121 digit probable prime:

11337.....751249

These seem near or at the limit of what I can aquire from the free Wolfram account with 1 minute loop limitation.

[danaj]

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 semi-prime 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.

[R.D. Silverman]

Originally Posted by danaj

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 semi-prime 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.

It would also be better if he would bother to actually respond to some of the queries. In particular, I
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.

[firejuggler]

Originally Posted by danaj

... 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. .

thats why I enquired about special form earlier.

just adding a note there : with 5 minutes, with tools already availlable to the public, 3^12311*6-1, 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*6-1 (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)

[a1call]

Originally Posted by Puzzle-Peter

I still have a copy of the latest Primo for Windows release that Marcel Martin did. It is lacking all the optimizations he did since then (2010), most notably the ability to run on several cores in parallel. So it is really slow compared to the Linux version. If you want to give it a try, let me know.

For speed comparison: Your 1073 digits number took 11 minutes to prove on a fairly average computer.

Thank you for the info Puzzle-Peter. Looks like schickel has been kind enough to do the run already. But thank you for the run-time info.

[Batalov]

Originally Posted by a1call

The 5121 digit Probable Prime is the evaluation of the expression (reconstructed from the code if not in error):
p=(42 x (61#-1))!^{(61# -1)}+61# x 48

If not in error? This "p" doesn't match the infamous 5121 digit "N" (which you have surprising trouble understanding not being a variable but "your" number), so there must be an error of some sort.

And why these weird contortions in the number's notation?
In general, (AB)!^(B) = A! B^A because it is simply = {AB}{(A-1)B}{(A-2)B}...B
so why not write it like that? For obfuscation?

[a1call]

Originally Posted by schickel

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.

[a1call]

Originally Posted by LaurV

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)^(n-1)", the fastest way to see if n is 2-PRP. Then "Mod(2,1088*n^3+1)^(1088*n^3)".

Alternatively, you can make a separate file, call it "test.gp", put inside

{ 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)
}

Wait...

Thank you LaurV,
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.

[chalsall]

Originally Posted by a1call

Thank you LaurV,

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".