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

[cheesehead]

Originally Posted by Mini-Geek

If I'm understanding Silverman's hint correctly,

Mini-Geek,

It would have been more instructive and useful for beyastard if you had encouraged beyastard to take Dr. Silverman's hint and do some work on his/her own, rather than just telling beyastard what you think the answer is.

You know -- the old "give a fish" / "teach to fish" distinction.

[cheesehead]

Originally Posted by Mini-Geek

If you try and fail at that, continue:

No, you're still giving an answer ("giving a fish") instead of showing how the effort of taking Silverman's hint is instructive ("how to fish"). The education will be in the effort of finding the prime, not in being told an answer.

beyastard has not yet shown us any evidence (e.g., range of integers searched, unsuccessfully, to find a prime not of that form) of having tried to use the hint. Once beyastard has done that, we can proceed to teaching what that failure means. OTOH, if beyastard succeeds ...

[R.D. Silverman]

Originally Posted by beyastard

The only reason I can think of why you would call this a pointless activity
is because you believe that one should not look into new areas of prime
number research but should do what everyone else already has.

I don't see why exploring new areas would be pointless

I will try to be gentle.

You admit that you are not a mathematician. Therefore you can not
possibly know what is new and what isn't new. Your claim that your
'research' is new therefore comes across as arrogance.

It is not 'new'. In fact, it is so elementary that it might be presented
as a simple homework problem in a first year number theory course.

I gave the perfect hint as to why what you are doing is pointless.
Follow this hint. Present a prime to this group that is NOT of your
form. Then ask yourself: "what is special about the prime that I just
presented".


May I suggest that you pick up and read any elementary number theory
book. Do the exercizes.

Your attempt at 'research' falls in the same category as someone without
a science education doing research into a cure for cancer.

[beyastard]

Originally Posted by R.D. Silverman

Your attempt at 'research' falls in the same category as someone without
a science education doing research into a cure for cancer.

It appears that a thread asking for help with a sieve so that searching for
large primes more efficiently has degraded into, basically, a thread of
belittling. Indirectly, it appears I am being told that as someone who does
not hold a Ph.D. in mathematics has no right to search for large primes.
If this is the case then GIMPS, et al, should not be open to the public but
be a private website. I will immediately quit GIMPS and delete Prime95
from all my computers as I am not "authorized" to assist in prime searches.

[R.D. Silverman]

Originally Posted by beyastard

It appears that a thread asking for help with a sieve so that searching for
large primes more efficiently has degraded into, basically, a thread of
belittling. Indirectly, it appears I am being told that as someone who does
not hold a Ph.D. in mathematics has no right to search for large primes.
If this is the case then GIMPS, et al, should not be open to the public but
be a private website. I will immediately quit GIMPS and delete Prime95
from all my computers as I am not "authorized" to assist in prime searches.

I never said that you had no RIGHT to conduct such a search.
I said that you had no QUALIFICATIONS.

One does not need a math PhD. One does need a knowledge
of basic number theory.

Finally, using computers to search for large primes, is not "research",
as you claimed to be doing. Your claim of "new research" was just
arrogance based upon ignorance. When I tried to lead you into actually
studying the mathematics of what you were doing, you chose not to
respond.

Don't let the door hit you on the way out.

[beyastard]

If you read my first post you will see it's nothing more than a request for
a sieve of a specific form as there are none that I can find. I see nothing
in my request that can even be closely considered showing arrogance.

Also, one does not have to have "qualifications" to use a piece of software
to sieve, test for prp then verify prp's as prime. One only needs to know how
to use the software.

Is it a requirement to have a basic understanding of computer hardware or software
to boot up a computer? Do you need to be "qualified" in networking to start
a browser and surf the internet? You merely need to know how to use the
software.

Again, the only thing I was searching for was assistance on a sieve of the
form I posted. If you read through my posts you will see I used the word "new"
in the context of a form that there is no sieves available for. Neither newpgen
nor multisieve handles these forms. I also stated that it appears that
there are many primes of this form. My first post was similar to that made
by robert44444uk. I've read the entire thread and seen nowhere mentioned
to him that searching for primes of the form a^(2^b)+(a+1)^(2^b) is
pointless. If a sieve exists for the form k*b1^n1*b2^n2+1 then it would
have been so much easier pointing me into the right direction. If there is
none my question was "can an existing one be modified to handle this
form?"

[Kevin]

Originally Posted by beyastard

If you read my first post you will see it's nothing more than a request for
a sieve of a specific form as there are none that I can find. I see nothing
in my request that can even be closely considered showing arrogance.

Have you ever considered that maybe there are no sieves of that form for a reason? And maybe that we've been trying to show you what that reason is for days now? And that maybe it's a little bit arrogant to ignore the advice of established mathematicians when you admit you have no experience in the area?

[geoff]

I am not a mathematician either, so perhaps someone can explain to me why searching for primes of the form k*3^3*5^2+1 say, is pointless but searching for primes of the form k*2^333333+1 is not? (Well, I know that k*2^333333+1 might be a Fermat Divisor, but apart from that?)

Since there are already sieves for k*2^n+1 (n fixed), albeit without source code, and lots of people using them, why would a sieve for k*b1^n*b2^m+1 (b1,b2,m,n fixed) be useless?

It can't be because all primes are of the form k * b1^n * b2^m + 1, because all primes are of the form k*2^n+1 too, and that doesn't make an ordinary fixed-n sieve pointless.

[TimSorbet]

Originally Posted by geoff

I am not a mathematician either, so perhaps someone can explain to me why searching for primes of the form k*3^3*5^2+1 say, is pointless but searching for primes of the form k*2^333333+1 is not? (Well, I know that k*2^333333+1 might be a Fermat Divisor, but apart from that?)

Since there are already sieves for k*2^n+1 (n fixed), albeit without source code, and lots of people using them, why would a sieve for k*b1^n*b2^m+1 (b1,b2,m,n fixed) be useless?

Remember Silverman's hint: find a prime that is not of this form. I'm going to try to find it myself, and if the OP posts what efforts he has made, I'll post my efforts as well.

Originally Posted by geoff

It can't be because all primes are of the form k * b1^n * b2^m + 1, because all primes are of the form k*2^n+1 too, and that doesn't make an ordinary fixed-n sieve pointless.

The definition of Proth numbers requires that 2^n be greater than k, so not all numbers are of the form k*2^n+1.

Edit: To the OP: can m and/or n equal 0? If so, the problem should be quite easy to spot. Whether they may or may not equal 0, this should have been specified clearly. Maybe that's all that RDS is complaining about, because at a quick glance I don't see anything wrong with it if m,n>0...

[geoff]

Originally Posted by Mini-Geek

Remember Silverman's hint: find a prime that is not of this form. I'm going to try to find it myself, and if the OP posts what efforts he has made, I'll post my efforts as well.

The definition of Proth numbers requires that 2^n be greater than k, so not all numbers are of the form k*2^n+1.

23 is a prime not of the form k*3^3*5^2+1. Why shouldn't someone search for those primes which are of this form? The sieve that was requested would allow them to do that efficiently.

[jrk]

Originally Posted by R.D. Silverman

I will try to be gentle.

RDS being gentle... That should really be appreciated.