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Yes, it is fairly low. A few bits lower and TF would have found it first.
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[QUOTE=c10ck3r;303806]
Yes, LaurV, it must be base 2. Base 10 would tell you how many digits it is, and base 59 would...just be stupid. Base 2 tells you how many bits. Also log2(factor) = x where 2^x=(factor)[/QUOTE] [strike]I hope your post was a joke. I was not arguing about log2() formula, but about log() formula. That is my "any base" against Dubslow's "base e". How about you read my post again and THINK about it...[/strike] edit: crosspost, saw the next (current) page where Dubslow answered already. |
LaurV, I was under the impression that your question was about the second half of Dubslow's post, not the first. For the first part, yes, it could be any base. He never said the first part was base 2, but instead base e, even though JH's generic formula is assumed to be base 10 without the presence of a listed base. If, as Dubslow suggested, log() was the natural logarithm, it would have been written ln().
Clarification- its a beautiful thing! |
[QUOTE=c10ck3r;303835]If, as Dubslow suggested, log() was the natural logarithm, it would have been written ln().[/QUOTE]
Not always. In fact, not often. In Perl, C, C++ and many, many other languages, log() returns the "natural logarithm". ln() doesn't exist. As James then pointed out, log(x)/log(base) will give you the number of digits in whatever base you desire. And, thus, you can create any of the other "log" functions using this formula. [QUOTE=c10ck3r;303835]Clarification- its a beautiful thing![/QUOTE] Indeed. :smile: |
log() meaning base ten or base e depends on who you ask and when. If you ask me when I'm writing out calculus by hand, I'll use ln() because it's shorter.
Wolfram Alpha generally assumes base e for log(), and uses log() for base e when displaying things. :smile: |
We learned in the school (that was early 80's last century) that if the base is 10, then is lg, if the base is e then is ln, and if the base is 2, then is lb. People use log when the base is implicit understood or when the base does not mater. In fact, a bit of google for "math standard notations" shows that this is also the way [URL="http://en.wikipedia.org/wiki/ISO_31-11"]ISO 31[/URL] defines the things (and I learned a new term, didn't know that the log[SUB]10[/SUB] is called "[URL="http://en.wikipedia.org/wiki/Common_logarithm"]common logarithm[/URL]" in English. See there too, about disambiguation of the notation).
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[QUOTE=Jwb52z;303612]Not too long ago, a few people explained to me the percentages between stage 1 and stage 2 of P-1 how factors are found. Knowing that, and maybe it is all just a coincidence, I am surprised because I have found 3 factors of numbers just today when all the time before I would go days between finding just one. Considering the percentage chance of finding a factor that is on screen when a new P-1 starts, it makes me kinda wonder how I could just have this much "good luck".[/QUOTE]Poisson(*) statistics. It's the same reason why buses apparently hunt in packs. You wait for ages for a bus and then three come along all at once.
Paul (*) As in one man's fish is another man's poisson. |
What, one man's fish is another man's fish?
And I had no idea there was a common logarithm, nor an ISO standard, nor have I ever seen lg or lb. Interesting standard though, would be useful if people actually knew about it. |
Stupid question (aside from my logarithm mess)...Is there a way to skip step 1 of P-1 on exponents that have, ie, b1=b2? Thanks!
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[QUOTE=c10ck3r;303958]Is there a way to skip step 1 of P-1 on exponents that have, ie, b1=b2?[/QUOTE]Yes, but only if you have the savefile from when the P-1 was already done. So in most cases: no.
And, if re-doing P-1, remember PrimeNet won't accept new P-1 results if the new B1 is smaller than the old B1, even if you did a "better" P-1 the second time by doing stage2 that wasn't done before. |
[QUOTE=James Heinrich;303962]Yes, but only if you have the savefile from when the P-1 was already done. So in most cases: no.[/QUOTE]
When doing continued / extended P-1 work, what from the previous P-1 savefile is used in the continued work? For instance, I do P-1 for an exponent with some B1 and B2 > B1, and keep the savefile. Then, I want to extend the work to B1new >= B1 and B2new > B2, B2new > B1new. What in the savefile gets re-used? Does this only help when B1new == B1, or also when B1new > B1 ? That is, what is the benefit of having the previous savefile? [QUOTE=James Heinrich;303962]And, if re-doing P-1, remember PrimeNet won't accept new P-1 results if the new B1 is smaller than the old B1, even if you did a "better" P-1 the second time by doing stage2 that wasn't done before.[/QUOTE] *nod* Did that once before. Ooops. |
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