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Search: Posts Made By: CRGreathouse
Forum: jwaltos 2020-10-30, 02:22
Replies: 5
Views: 170
Posted By CRGreathouse
In number theory it's all a matter of definition,...

In number theory it's all a matter of definition, of course. But in abstract algebra this is life or death -- you have lots of groups, rings, fields, etc. with units and it's important to agree on...
Forum: Number Theory Discussion Group 2020-10-27, 14:08
Replies: 27
Views: 852
Posted By CRGreathouse
Actually, I don't think that's surprising at all....

Actually, I don't think that's surprising at all.



I don't think that's surprising either. Both of these are totally ordinary and expected. Estimating exactly how large isn't particularly easy,...
Forum: Number Theory Discussion Group 2020-10-26, 19:30
Replies: 27
Views: 852
Posted By CRGreathouse
There are 446 primes up to 3159, so 14.1%. There...

There are 446 primes up to 3159, so 14.1%. There are 422 numbers coprime to 1, 2, ..., 99, or 13.4%. What does this show? 3159 isn't a counterexample to the second Hardy-Littlewood conjecture. But...
Forum: Prime Gap Searches 2020-10-23, 16:56
Replies: 108
Views: 11,473
Posted By CRGreathouse
Borel-Cantelli gives good intuition for where to...

Borel-Cantelli gives good intuition for where to start, but the whole point of the paper is that the primes have more subtle behavior than the Cramer distribution would have you believe (which we've...
Forum: Puzzles 2020-10-23, 03:23
Replies: 26
Views: 718
Posted By CRGreathouse
That eBay pin is strikingly similar. Tracking it...

That eBay pin is strikingly similar. Tracking it down is surely the key. Is there a series of pins with different symbols in the front raised area?
Forum: Number Theory Discussion Group 2020-10-22, 17:06
Replies: 27
Views: 852
Posted By CRGreathouse
It's like looking for twin primes: sure, if you...

It's like looking for twin primes: sure, if you look really high they're rare, but no one doubts that there are plenty of them, even though they're really close together.
Forum: Number Theory Discussion Group 2020-10-22, 14:32
Replies: 27
Views: 852
Posted By CRGreathouse
That case is certain: you can't fit that many...

That case is certain: you can't fit that many primes into a run of 30 except at the beginning. But there are higher cases where the first conjecture says there is a really tight configuration, so...
Forum: Miscellaneous Math 2020-10-17, 04:43
Replies: 9
Views: 307
Posted By CRGreathouse
As opposed to what other kind of prime numbers?...

As opposed to what other kind of prime numbers? :confused:
Forum: Math 2020-10-09, 13:14
Replies: 2
Views: 156
Posted By CRGreathouse
There's nothing in this method that limits it to...

There's nothing in this method that limits it to primorials.

If you push a little further you'll get the Legendre sieve and hence the beginnings of sieve theory. :smile:
Forum: Computer Science & Computational Number Theory 2020-10-08, 19:56
Replies: 48
Views: 9,528
Posted By CRGreathouse
w00t Fantastic!

Fantastic!
Forum: Miscellaneous Math 2020-09-24, 20:28
Replies: 56
Views: 2,544
Posted By CRGreathouse
I move many threads to Misc Math. I haven't yet...

I move many threads to Misc Math. I haven't yet abused my power to rename threads (though I have occasionally renamed threads with vague or misleading titles to be more explanatory, albeit bland).
Forum: Miscellaneous Math 2020-09-24, 19:33
Replies: 56
Views: 2,544
Posted By CRGreathouse
Grantham has an explicit finite set he...

Grantham has an explicit finite set he conjectures to contain a number which is both a Carmichael number and a Lucas pseudoprime, see A018188 (https://oeis.org/A018188).
Forum: Miscellaneous Math 2020-09-22, 18:09
Replies: 56
Views: 2,544
Posted By CRGreathouse
It takes me > 10 minutes to test the composites...

It takes me > 10 minutes to test the composites up to 3000. :blush: Perhaps someone else can do better.

th2(p)=my(u='u,b=(Mod([1,1;1,u],p)^p)[1,2]); b==subst(b,u,p-u+2)
Forum: Analysis & Analytic Number Theory 2020-09-22, 14:21
Replies: 8
Views: 761
Posted By CRGreathouse
:bow:

:bow:
Forum: Alberico Lepore 2020-09-18, 17:58
Replies: 22
Views: 1,569
Posted By CRGreathouse
Sure, if you have enough information about the...

Sure, if you have enough information about the factor. If you don't know anything about the factors then it's much slower than other methods.
Forum: Prime Gap Searches 2020-09-18, 17:48
Replies: 108
Views: 11,473
Posted By CRGreathouse
I wouldn't say that, but I don't really...

I wouldn't say that, but I don't really understand what you're trying for here. The point of the paper was to give a heuristic which significantly improves upon Cramer; why would you analyze it with...
Forum: Miscellaneous Math 2020-09-17, 15:42
Replies: 56
Views: 2,544
Posted By CRGreathouse
Has anyone coded this in PARI/GP so we can test...

Has anyone coded this in PARI/GP so we can test various ranges?
Forum: Miscellaneous Math 2020-09-16, 19:18
Replies: 56
Views: 2,544
Posted By CRGreathouse
This sounds very much like a pseudoprime test, if...

This sounds very much like a pseudoprime test, if I understand your English.
Forum: Factoring 2020-09-16, 14:34
Replies: 6
Views: 439
Posted By CRGreathouse
:goodposting:

:goodposting:
Forum: Miscellaneous Math 2020-09-16, 03:25
Replies: 56
Views: 2,544
Posted By CRGreathouse
I'm not sure what there is to understand. You...

I'm not sure what there is to understand. You posted a test which looked like a probable prime test. On examination, it seems like primes pass it, most composites fail, and some composites pass. This...
Forum: Factoring 2020-09-16, 03:19
Replies: 8
Views: 547
Posted By CRGreathouse
It does act, in many ways, like a random...

It does act, in many ways, like a random algorithm. (In fact, the paper introducing it described it as a Monte Carlo method.) But as LaurV said, it is in fact completely deterministic.
Forum: Lounge 2020-09-15, 03:33
Replies: 1,127
Views: 54,927
Posted By CRGreathouse
It's a Hobson's choice: take the precautions,...

It's a Hobson's choice: take the precautions, save lives, and take a hit to the economy, or else fail to take precautions, people die, and the economy takes a hit anyway.
Forum: Lounge 2020-09-15, 01:11
Replies: 1,127
Views: 54,927
Posted By CRGreathouse
There's definitely cross-reactivity from various...

There's definitely cross-reactivity from various cornaviruses, I wouldn't say cross-immunity. I don't know the particular paper you're referencing, though.



Given that COVID-19 causes...
Forum: Lounge 2020-09-14, 19:01
Replies: 1,127
Views: 54,927
Posted By CRGreathouse
I haven't seen evidence of that, but that sounds...

I haven't seen evidence of that, but that sounds pretty exciting.
Forum: Lounge 2020-09-14, 17:15
Replies: 1,127
Views: 54,927
Posted By CRGreathouse
I definitely agree that the programs have...

I definitely agree that the programs have disincentivized work, and may continue to do so. There have been plenty of articles about people being angry at their small business owners for applying for...
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