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Search: Posts Made By: CRGreathouse
Forum: Miscellaneous Math 2020-10-17, 04:43
Replies: 9
Views: 260
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: 139
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: 45
Views: 9,161
Posted By CRGreathouse
w00t Fantastic!

Fantastic!
Forum: Miscellaneous Math 2020-09-24, 20:28
Replies: 56
Views: 2,199
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: 2,199
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: 2,199
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: 541
Posted By CRGreathouse
:bow:

:bow:
Forum: Alberico Lepore 2020-09-18, 17:58
Replies: 22
Views: 1,360
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: 91
Views: 10,369
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: 2,199
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: 2,199
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: 379
Posted By CRGreathouse
:goodposting:

:goodposting:
Forum: Miscellaneous Math 2020-09-16, 03:25
Replies: 56
Views: 2,199
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: 462
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: 1,124
Views: 52,655
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: 1,124
Views: 52,655
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: 1,124
Views: 52,655
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: 1,124
Views: 52,655
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...
Forum: Miscellaneous Math 2020-09-13, 06:12
Replies: 8
Views: 456
Posted By CRGreathouse
In that case, I don't find any examples below the...

In that case, I don't find any examples below the unfactored composite Mp = 2^1213 - 1.
Forum: Miscellaneous Math 2020-09-13, 04:04
Replies: 3
Views: 263
Posted By CRGreathouse
What are you taking the log of? If it's just the...

What are you taking the log of? If it's just the zeta, I don't get convergence. If it's the whole inner sum, what branch are you taking?
Forum: Miscellaneous Math 2020-09-13, 02:05
Replies: 8
Views: 456
Posted By CRGreathouse
2*2^2-1 | 2^3-1

2*2^2-1 | 2^3-1
Forum: Alberico Lepore 2020-09-10, 00:47
Replies: 22
Views: 1,360
Posted By CRGreathouse
[$]ab \equiv 1 \pmod4,[/$] so either [$]a \equiv...

[$]ab \equiv 1 \pmod4,[/$] so either [$]a \equiv b \equiv 1 \pmod4[/$] or [$]a \equiv b \equiv 3 \pmod4[/$].



[$$]2ab + 2a^2 + (b^2 - 2ab + a^2)/4 = (9a^2 + 6ab + b^2)/4[/$$]

Yep, this...
Forum: Miscellaneous Math 2020-09-09, 04:02
Replies: 3
Views: 311
Posted By CRGreathouse
I believe the first prime p for which all three...

I believe the first prime p for which all three numbers are not only composite, but for which all numbers within 100 of each are composite is p = 64516043. I imagine these primes should have density...
Forum: Information & Answers 2020-09-07, 02:44
Replies: 38
Views: 7,527
Posted By CRGreathouse
Alternate construction: by Bertrand's postulate...

Alternate construction: by Bertrand's postulate (proven by Chebyshev, re-proven by Ramanujan and many others), there is a prime between every two Mersenne numbers.
Forum: Alberico Lepore 2020-09-06, 00:19
Replies: 15
Views: 830
Posted By CRGreathouse
I hope you and your family are well. Take as long...

I hope you and your family are well. Take as long as you need.
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