Sieve needed for k*b1^m*b2^n+1

[beyastard]

Originally Posted by R.D. Silverman

I am still curious as to why the OP thinks that finding new primes by blindly using someone else's software is 'research'.

My words were "... new areas of prime number research.." when I meant to
say "... new areas of prime number searches...," simply a mistake of
words on my part.

Also I stated, "... but I research prime numbers..." which I do when I have
time but have found nothing that is already known, so nothing to post
about that.

As for "blindly using someone else's software," lead me to sources I can study
to learn to write my own sieve's and I'll do it all myself. Further, I've never
called prime searching as research.

As for cheeseheads comment, "But your homework assignment wasn't to
download PDFs; it was to try to find a prime that was not of the form you
stated in your OP." Doc said, "May I suggest that you pick up and read
any elementary number theory book. Do the exercizes." And so I followed
his suggestion and did so and am reading them as time permits.

And finally, for the remainder of the "assignments," I am currently working
on them, again, as time permits.

[beyastard]

Originally Posted by R.D. Silverman

So? Other than being a stamp collection, please explain the value
of increasing the number of known large primes. What will you do with these
primes? What mathematics will be learned? What problems will they help
solve? What algorithms will be improved by searching for them?

Then projects such as GIMPS, et al, are a waste of time and many people
are doing useless searches for such primes.

[beyastard]

Originally Posted by Mini-Geek

Run -f file.txt and PFGW will attempt to trial factor every number (to an automated depth) before PRPing it. Read pfgwdoc.txt to learn about the other options and how to tweak how much TF it tries.

Yes, that is what I have been doing, thought it is still quite slow.

[R.D. Silverman]

Originally Posted by beyastard

My words were "... new areas of prime number research.." when I meant to
say "... new areas of prime number searches...," simply a mistake of
words on my part.

Bull.

Congratulations. You just made my "willfully ignorant" ignore list.

[R.D. Silverman]

Originally Posted by beyastard

Then projects such as GIMPS, et al, are a waste of time and many people
are doing useless searches for such primes.

On the contrary. GIMPS has spurred much research into algorithms
and has led to the irrational-base DWT that is now used. The
effort to develop code also taught us many things.

The primes themselves are not very useful at all. Finding them is certainly
FUN, but finding a new one or even several new ones will not advance
our understanding of the underlying mathematics. OTOH, the continued
search for better algorithms has great value.

You on the other hand have made it clear that you are not interested in
the algorithms. It is also clear that you lack the background to make
a contribution towards improved algorithms. You simply want someone else's
code handed to you.

<plonk>

[10metreh]

Originally Posted by beyastard

Then projects such as GIMPS, et al, are a waste of time and many people
are doing useless searches for such primes.

GIMPS are searching for a prime of the form 2^p-1. There are very few of these, and they can be tested much higher than other numbers using the Lucas-Lehmer test. This means that most of the time the largest known prime number is of the form 2^p-1. Same with the other projects. They are not searching for virtually "random" primes, since this would be very easy and very boring. There would be no thrill, as you would find so many primes.

P.S. Dr Silverman's ignore list is very long. I'm one of the hundreds on it. If you join this forum and ask lots of questions, you will end up on it. He is on my ignore list for insulting me.

[beyastard]

Originally Posted by R.D. Silverman

On the contrary. GIMPS has spurred much research into algorithms
and has led to the irrational-base DWT that is now used. The
effort to develop code also taught us many things.

The primes themselves are not very useful at all. Finding them is certainly
FUN, but finding a new one or even several new ones will not advance
our understanding of the underlying mathematics. OTOH, the continued
search for better algorithms has great value.

You on the other hand have made it clear that you are not interested in
the algorithms. It is also clear that you lack the background to make
a contribution towards improved algorithms. You simply want someone else's
code handed to you.

<plonk>

You're arrogance knows no bounds, does it? I have taken your suggestions
and have been studying as well as working on your "assignments" at every
opportunity. You should try not to be so opinionated and make assumptions
that contradict other peoples statements. Did I not say I'd do it myself once
I know the basic algorithms involved? Do you recall in one of my posts I
stated "also, if I am able to learn the 'mechanics' of sieves, I'd tackle this
problem myself" and did I not say that I took your suggestions and am
studying elementary number theory? Already, I am in the planning stages
of writing this sieve myself.

Also, I have found a copy of Knuth vol II as you suggested (as well as vols
I and III). I really don't know how much more clear I can make it to you
when you won't even listen to what I'm saying. Maybe I should just be
blunt and say it in simple language so that you may understand.

I am studying elementary number theory and am writing my own sieve
for this form.

I hope that statement is clear enough for you to understand. It is not my
intention to be rude, I am simply trying to get this across to you. I am,
also, trying to get it across to you that I have been taking your suggestions
and working out solutions for myself. If you wish to ignore me from this point
on, well, I'd like to thank you for your input as it has led me to a better
understanding and helped me to initiate more in-depth study into
number theory.

[cheesehead]

Originally Posted by beyastard

As for cheeseheads comment, "But your homework assignment wasn't to download PDFs; it was to try to find a prime that was not of the form you stated in your OP." Doc said, "May I suggest that you pick up and read any elementary number theory book. Do the exercizes." And so I followed his suggestion and did so and am reading them as time permits.

Yes, I overlooked the need to specify first assignment. :-)

[cheesehead]

Originally Posted by beyastard

You're arrogance knows no bounds, does it?

< snip >

I'd like to thank you for your input as it has led me to a better understanding and helped me to initiate more in-depth study into number theory.

Having supported Dr. Silverman's mathematical hint, let me balance that by saying that Dr. Silverman has nowhere near the ability to educate novices appropriately in a public forum as he does to do the math itself.

It's not arrogance (he can walk the walk); it's inability to modulate his message to communicate with students much below his level, in my opinion. He's actually mellowed a bit recently (though I don't necessarily expect you to believe that without having scanned the archives).

[beyastard]

Originally Posted by cheesehead

Having supported Dr. Silverman's mathematical hint, let me balance that by saying that Dr. Silverman has nowhere near the ability to educate novices appropriately in a public forum as he does to do the math itself.

It's not arrogance (he can walk the walk); it's inability to modulate his message to communicate with students much below his level, in my opinion. He's actually mellowed a bit recently (though I don't necessarily expect you to believe that without having scanned the archives).

Thanks for your input cheesehead. I hold absolutely no animosity toward
the Doc but continue to respect him thought I, at times, get frustrated
trying to get my point acrossed. Also, to validate my last post I am showing
how far I have got in a siev of this form. It appears more simple than I have
originally anticipated. The basic algorithm is as follows in pseudocode:

// sieve algorithm for k*b1^n1*b2^n2+1
// where k, b1, n1, b2 are fixed and n2 is variable
//
// ...simplified PSEUDOCODE...
//
// get input from user/file for terms
BEGIN
    GetInput();
    if(k%b1 OR k%b2)
        print("Error: k shares factor with b1 or b2")
        exit
    // initialize bitmap
    // for this example, we will simplify it by using a bytemap
    for(i=0; i<maxn; i++)
        bitmap[i] = 0  // clear all bits
    // initialize values
    k1 = k*b1^n1
    p = minp     // set p to minimum p
    n = minn     // set n to minimum n we are sieving
    // begin sieve
    do
        if(k1*b2^n2+1 % p)
            setbit(bitmap[i])       // composite
            // remove all remaining candidates that share factor
            while(i <= maxn)
                i += p-1
                setbit(bitmap[i])
        NextPrime(p)
        i = 0
    while(p != maxp OR UserInterrupt)
END

As this is a rough first draft at an algorithm for this sieve there may be
parts I've left out. As I continue to develop this code I will be sure to
keep anyone who's interested posted on my progress.

And again, I'd like to give my thanks to the Doc

[beyastard]

I noticed an error in my pseudocode.
If k = 2 then p-1 becomes (p-1)/2

// begin sieve
    do
        if(k1*b2^n2+1 % p)
            setbit(bitmap[i])       // composite
            // remove all remaining candidates that share factor
            while(i <= maxn)
            if(k == 2)
                i += (p-1)/2
            else
                i += p-1
            setbit(bitmap[i])
        NextPrime(p)
        i = 0
    while(p != maxp OR UserInterrupt)

Instead of checking whether or not the bit is set or not, I just set it to
speed it up by getting rid of cmp and jxx instructions as all are composite.