The inimitable RDS
 

[QUOTE=KEP;301294]10^999999+y (y=>1 to y<=5M) is sieved to p=2P with 80310 candidates remaining. The sieving is optimal for y~=2.7M :smile:

Sieving is currently paused and wont resume untill we gets near y=2.7M and will obviously never resume if a PRP is found for y<2.7M ... well let's see what the future holds.

Take care

Kenneth[/QUOTE]

This task is a [b]hopeless[/b] waste of time. You might be able to find the first PRP
greater than 10^6, although what value the computation might have is
beyond me.

But proving it prime is so far beyond what current computers and algorithms
can do that even attempting it is ridiculous.

[QUOTE=R.D. Silverman;301324]This task is a [B]hopeless[/B] waste of time. You might be able to find the first PRP
greater than 10^6, although what value the computation might have is
beyond me.

But proving it prime is so far beyond what current computers and algorithms
can do that even attempting it is ridiculous.[/QUOTE]

Challenge accepted. The first PRP above 10^6 is 1000003. My computer has proven it's primality. Next time, proof your message please. XD

'Bout time I proved you wrong :)

[QUOTE=c10ck3r;301330]Challenge accepted. The first PRP above 10^6 is 1000003. My computer has proven it's primality. Next time, proof your message please. XD

'Bout time I proved you wrong :)[/QUOTE]

10^6 digits.......

[QUOTE=R.D. Silverman;301324]This task is a [b]hopeless[/b] waste of time. You might be able to find the first PRP greater than 10^6, although what value the computation might have is beyond me.

But proving it prime is so far beyond what current computers and algorithms
can do that even attempting it is ridiculous.[/QUOTE]Not [b]strictly[/b] true.

It may be that the (recursive) factorization of p \pm 1 is possible with current computers and algorithms. The likelihood of that being the case is somewhere between nil and negligible.

The value of the computation, IMO, is bragging rights. Look at me, I won the jackpot!

Paul

[QUOTE=xilman;301338]Not [b]strictly[/b] true.

It may be that the (recursive) factorization of p \pm 1 is possible with current computers and algorithms. The likelihood of that being the case is somewhere between nil and negligible.

The value of the computation, IMO, is bragging rights. Look at me, I won the jackpot!

Paul[/QUOTE]

One gets bragging rights if and only if the discoverer used his/her OWN
software.

[QUOTE=R.D. Silverman;301343]One gets bragging rights if and only if the discoverer used his/her OWN
software.[/QUOTE]

Well, some people are the brains, others are the muscle. Usually it takes both to get the job done.

[QUOTE=R.D. Silverman;301343]One gets bragging rights if and only if the discoverer used his/her OWN software.[/QUOTE]One gets bragging rights by bragging. Whether you think that's justified is beside the point. Whether anyone is impressed by the bragging is similarly dependent on the bragger and the subject about which the bragging takes place.

[QUOTE=R.D. Silverman;301343]One gets bragging rights if and only if the discoverer used his/her OWN
software.[/QUOTE]

Oh dear oh dear... Mr. Silverman, I almost didn't consider this worth an answer. I just don't seem able to ever grasp why you have to write this way and make other peoples effort seem redundant or pointless. First of all, not just for me but also for other people (of witch some is not yet born) this will be a challenge worth the effort. For instance we have the whole "Borderprime/Borderprp" collection, wich will benefit from this search. Also if we have a MegaPRP candidate that will return a strong-PRP in any fermbase<=100 then according to some users on this board, if the Rhiemann-hypotheses can be proven correct we will know for sure that we have the lowest possible megaprime. However if no-one ever cared to do such a search for the lowest possible megaprime, we would really never know what numbers to start working on, in order to conclusively state that it is in fact (according to the Rhiemann hypothesis) a PRIME. I care, not because it may be a hard task to prove the PRP actually is prime, but because I'm also curious to see if someday something usefull (as in not pointless) can come out of such a MegaPRP.

If at least nothing usefull or something better (as referred to) comes from the world of math a "strong-MegaPRP" of interest might actually help encourage software developers to extend the limits of current programs like PRIMO, such that a distributed effort can be used to attack the PRP and produce a valid and conclusive solution to tell weather or not the PRP is in fact a prime or a bonifide composite. Eitherway if nothing better comes from math or from software, at least it can work as good entertainment, since these tests is considerably short and will take almost the same time the entire way through the testrange. A test currently will take only 10 hours on a Q6600 and about 4 h 20 m on an I5 K2300.

Last but not least. It is always better to say nothing at all, if you've nothing good to say. I've spend almost 1000 CPU days on this effort (maybe more), so I really don't like the way you influence people who might consider to support the effort, by forinstance calling it a pointless effort. I do believe that even though all of us has a limited timespan in ones duration of life, at least within resonable time, from the time we have the PRP, till someone can answer the question "How to prove it?" is limited and may in fact very well be within most of our lifespans. Eventhough the answer to the question may never come if everyone considers it pointless to try to answer it or limits themself in their attempt to answer :smile:

Weather or not you will support this effort is entirely up to you, but please stop the flaming, because at least to some people this effort has a value.

Take care

Kenneth

[QUOTE=KEP;301357]Oh dear oh dear... Mr. Silverman, I almost didn't consider this worth an answer. I just don't seem able to ever grasp why you have to write this way and make other peoples effort seem redundant or pointless.
[/QUOTE]

Because it takes very little intelligence to run software written by
other people. It deserves very little credit.

[QUOTE]
First of all, not just for me but also for other people (of witch some is not yet born) this will be a challenge worth the effort. For instance we have the whole "Borderprime/Borderprp" collection, wich will benefit from this search. Also if we have a MegaPRP candidate that will return a strong-PRP in any fermbase<=100 then according to some users on this board, if the Rhiemann-hypotheses can be proven correct we will know for sure that we have the lowest possible megaprime.

[/QUOTE]

Your knowledge of the mathematics involved is faulty and on a level
with your spelling. Finding a strong PRP in a single Fermat base does
not prove primality, even if ERH (Extended Riemann Hypothesis) is
correct. And just proving RH does not help at all here. I will bet that
you don't even know the difference between RH and ERH.
[QUOTE]


However if no-one ever cared to do such a search for the lowest possible megaprime, we would really never know what numbers to start working on, in order to conclusively state that it is in fact (according to the Rhiemann hypothesis) a PRIME.

[/QUOTE]

This is nonsensical gibberish.

[QUOTE]
I care, not because it may be a hard task to prove the PRP actually is prime, but because I'm also curious to see if someday something usefull (as in not pointless) can come out of such a MegaPRP.
[/QUOTE]

what has 10^6 digits got to do with anything you suggest that 10^5 or 10^4
digits would not??? Answer: NOTHING

[QUOTE]
If at least nothing usefull or something better (as referred to) comes from the world of math a "strong-MegaPRP" of interest might actually help encourage software developers to extend the limits of current programs like PRIMO,
[/QUOTE]

Extending PRIMO is not going to help find million-digit primes.

You don't seem to get it: Finding an arbitrary million digit prime is [b]SO FAR
OUT OF REACH[/b] that the effort is pointless unless better algorithms
come along.

[QUOTE]
such that a distributed effort can be used to attack the PRP and produce a valid and conclusive solution to tell weather or not the PRP is in fact a prime or a bonifide composite. Eitherway if nothing better comes from math or from software, at least it can work as good entertainment,
[/QUOTE]

If you find it entertaining, go ahead. You'd have a better chance
at winning the lottery.


[QUOTE]

Last but not least. It is always better to say nothing at all, if you've nothing good to say.
[/QUOTE]

But I DO have something good to say. I'm trying to dissuade mathematically
ignorant people from pursuing a futile effort. And finding the prime itself adds
no value to mathematics. A new algorithm might, but the prime itself
is a mere numerical curiosity.

[QUOTE]
I've spend almost 1000 CPU days on this effort (maybe more), so I really don't like the way you influence people who might consider to support the effort, by forinstance calling it a pointless effort.
[/QUOTE]

Too bad. I really don't like the way ignorant people pursue hopeless
projects when there are many projects that are NOT hopeless.

Finally, I am qualified to judge the merits of an effort in computational
number theory. You are not. If you think you are you can tell us:

(1) Where you got your math degree
(2) Where you got your graduate degree
(3) What papers you have published
(4) What number-theory or related conferences have invited you to give
talks
(5) What journals have asked you to referee papers. This is perhaps the
most important form of respect that there is from colleagues: That they
believe you sufficiently qualified to referee the work of others.


[QUOTE]
Weather or not you will support this effort is entirely up to you, but please stop the flaming, because at least to some people this effort has a value.
[/QUOTE]

I am not flaming. I am giving a professional evaluation as to the
worth of a computation. It is a sign of your immaturity that you see it
as flaming.

Finally, allow me to ask: If you think one deserves credit for running
code written by others (and for which you did not have the necessary
expertise) do you also think a student deserves credit for plagiarized work?
Because that is what it is. You are taking the intellectual effort of others
that you yourself could not achieve and using those efforts to claim
your own credit for some purely numerical curiousity found by the code.

[QUOTE=R.D. Silverman;301376]Because it takes very little intelligence to run software written by other people. It deserves very little credit.
[/QUOTE]

Totally wrong. Discoverer gets all credits even if his role was only to run a computer. He may share credits of his discovery with a programmer, if he wants.



[QUOTE=R.D. Silverman;301376] And finding the prime itself adds
no value to mathematics.
[/QUOTE]

You forgot to add that it is about mathematics that you represent.


[QUOTE=R.D. Silverman;301376] Too bad. I really don't like the way ignorant people pursue hopeless projects when there are many projects that are NOT hopeless.
[/QUOTE]

You don't know him and you call him ignorant. Few sentences he wrote cannot be a base for such statement (even if there are mistakes or wrong ideas, which can happen to anybody including you).




[QUOTE=R.D. Silverman;301376] Because that is what it is. You are taking the intellectual effort of others that you yourself could not achieve and using those efforts to claim your own credit for some purely numerical curiousity found by the code.
[/QUOTE]


Programs were written and distributed for this purposes. For other people to make their own discoveries. So, don't accuse people of crimes they did not commit.

[QUOTE=literka;301381]Programs were written and distributed for this purposes. For other people to make their own discoveries. So, don't accuse people of crimes they did not commit.[/QUOTE]

I wonder if Mr. Silverman wrote the operating system he runs his software on. Or the compiler used to compile it. Or designed and built the CPUs which execute his code. Or designed and built the generator which powers his systems. Or discovered and refines the fuel for the generator. Or, or, or....