[QUOTE=3.14159;225089]Wow. That was all that it was? A tautology/circular argument? :lol:![/QUOTE]

That's what I expected when it was brought up -- and I imagine I said as much on this thread (though I'm not going to go digging back through to look for it). But there's a

[QUOTE=3.14159;225089]I suspect it of being a kook site, but, seeing as their applets work correctly to some extent, I am undecided on that matter.[/QUOTE]

They're trying pretty hard to look like kooks, but perhaps they're not. I'll have a look at their code. VB... [i]shudder[/i].

[QUOTE=3.14159;225092]Call the press! We're going to be filthy rich!

Amirite?[/QUOTE]

I expect to see the royalty checks coming for sm88 soon enough. After that, fast cars and women lined up 'round the block. But I'll be happy to bask in the reflected glory.

All kidding aside, though, the discovery did pan out -- it just didn't end up giving additional insight or faster techniques. What's more, sm88 is better able to express his mathematical ideas. Surely you find post #297 easier to understand than post #28? So there has been serious progress. And of course he also now knows how to use Pari.

[QUOTE=3.14159;225092]CRG, have you managed to do some testing on 25326001 using that app? Does it say that it's a 7-SPRP?[/QUOTE]

I downloaded the source code and I'm looking it over. It's interesting -- almost all of the math wasn't written by the naturalnumbers guy, but rather by a David Ireland who actually knows some math (though he's clearly not a mathematician, and his code is not fast). The difference between the different parts of the code is crazy.

But I haven't actually run the program yet.

[QUOTE=CRGreathouse]That's what I expected when it was brought up -- and I imagine I said as much on this thread (though I'm not going to go digging back through to look for it). But there's a
[/QUOTE]

It looks as if this sentence is unfinished. If so, what did you intend to post?

[QUOTE=CRGreathouse]I expect to see the royalty checks coming for sm88 soon enough. After that, fast cars and women lined up 'round the block. But I'll be happy to bask in the reflected glory.
[/QUOTE]

We'll be celebrities! We'll be known as math geniuses everywhere! We'll become household names!

[QUOTE=CRGreathouse]All kidding aside, though, the discovery did pan out -- it just didn't end up giving additional insight or faster techniques. What's more, sm88 is better able to express his mathematical ideas. Surely you find post #297 easier to understand than post #28? So there has been serious progress. And of course he also now knows how to use Pari.
[/QUOTE]

Admittedly, he did make some progress in expressing his ideas. I was surprised you were able to understand what he meant most of the time.

[QUOTE=CRGreathouse]I downloaded the source code and I'm looking it over. It's interesting -- almost all of the math wasn't written by the naturalnumbers guy, but rather by a David Ireland who actually knows some math (though he's clearly not a mathematician, and his code is not fast).[/QUOTE]

In the site, Ross claims:

[QUOTE=Michael M. Ross](Modular exponentiation code provided by DI Management Cryptography Software.)[/QUOTE]

[QUOTE=CRGreathouse]They're trying pretty hard to look like kooks, but perhaps they're not. I'll have a look at their code. VB... shudder.
[/QUOTE]

Just read their article on Fermat's factoring method: They claim they made improvements to the method, and you can view those [URL="http://www.naturalnumbers.org/fixfermatfact.html"]here[/URL].

[QUOTE=3.14159;225104]It looks as if this sentence is unfinished. If so, what did you intend to post?[/QUOTE]

I did get cut off there (accidental shift-end, I imagine), but I continued the thoughts in the next post.

[QUOTE=3.14159;225104]Just read their article on Fermat's factoring method: They claim they made improvements to the method[/QUOTE]

I saw that too. The 'improvements' look like the usual way it's used, and Fermat's method is basically worthless with or without improvements. (It does lead to better methods, eventually up to the NFS -- but on its own it's far too slow.)

[QUOTE=CRGreathouse]I saw that too. The 'improvements' look like the usual way it's used, and Fermat's method is basically worthless with or without improvements. (It does lead to better methods, eventually up to the NFS -- but on its own it's far too slow.)
[/QUOTE]

It is useless for any numbers larger than about 10-12 digits. Trial division is better than it.

[QUOTE= Kook]*OK, I acknowledge that trial div still has the edge for this baby example. Obviously, try something bigger for a fair test, say 9 or 10 digits. Remember that we're interested in the difficult ones - those with only 2 prime factors that are similar in size to the square root. A systematic survey by magnitude will be coming soon.
[/QUOTE]

10 digits? TD can find such a number's factors instantly. One of his own apps takes about a tenth of a second to find a p5. Fermat's is useless.

Another thing to ponder: Can QS be done, manually, w/no compy help, given enough time and knowledge of how it works (And maybe a large enough sheet of paper and a pen with plenty of ink)?

That would make decent headlines:

[QUOTE=Imaginary Headlines:]
Attention: A world record has been broken! Mr. Joe Smith has successfully split the c37 number 3868201127095457574466947223184535677 into its prime factors, with no computer assistance!:

[B]92734364657447299 * 41712704253533812223 ! [/B]

It took him 45 days to accomplish this. Mr. Joe Smith is looking forward to his $1500 reward.

[/QUOTE]

P.S: And no, I do not mean "41712704253533812223 factorial"

So, all circular stuffs aside:

Still conducting the prime searches for a ≈119000-digit prime and a 257920-digit prime. (Using bases 2 and 798336)

What is the knowledge on A165223 I know it's Products of 2 successive Mersenne primes. I want to know about something known before I post.

I know nothing special about that sequence. Essentially the only way to compute terms is to find all the Mersenne primes in a given range.

I can say things based on my knowledge of Mersenne primes, though. For example, for n > 2, a(n+1) > 64a(n).

I find all the terms except the first have a digital root of 4 or 1 just like the Mersenne primes >7 if we could confirm something like a pattern (I think starting at the 4th term they may take on the opposite to the series for the Mersenne primes>31) if this was ever proven true it could let us look 4 Mersenne primes in the future(that's why I'm doubtful).

[QUOTE=science_man_88]I find all the terms except the first have a digital root of 4 or 1 just like the Mersenne primes >7 if we could confirm something like a pattern (I think starting at the 4th term they may take on the opposite to the series for the Mersenne primes>31) if this was ever proven true it could let us look 4 Mersenne primes in the future(that's why I'm doubtful).
[/QUOTE]

The law of small numbers, at work again. Unless you can definitively prove this, it is nothing more than a guess.