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Forum: Miscellaneous Math 2020-09-18, 12:12
Replies: 7
Views: 215
Posted By Dr Sardonicus
About the small sample size, me three. ...

About the small sample size, me three.

Benford's law is based on the theorem that, if α is a (positive) real irrational number, the fractional parts of α, 2*α, 3*α, etc are uniformly distributed...
Forum: Lounge 2020-09-17, 13:50
Replies: 42
Views: 1,678
Posted By Dr Sardonicus
The REAL plant experts

I'm generally fairly good -- at least, for a layman -- at plant ID's. With common weeds or garden plants, I can often get the genus right, even if I can't name the species.

But I have just been...
Forum: Miscellaneous Math 2020-09-17, 13:17
Replies: 24
Views: 3,545
Posted By Dr Sardonicus
General guidelines have already been supplied...

General guidelines have already been supplied here (https://www.mersenneforum.org/showpost.php?p=557143&postcount=23). Heed them.

For information more specific to a given subforum, click on that...
Forum: Miscellaneous Math 2020-09-17, 12:47
Replies: 35
Views: 1,067
Posted By Dr Sardonicus
Regarding the use of polynomial coefficients to...

Regarding the use of polynomial coefficients to prove primality, there is already a well-known deterministic test, the AKS primality test. See the following 2004 paper...
Forum: Soap Box 2020-09-16, 14:09
Replies: 29
Views: 1,305
Posted By Dr Sardonicus
Sounds good! Oh, wait. Allow the medical...

Sounds good!

Oh, wait. Allow the medical system to grow naturally? The AMA is calling on Line Two....
Forum: Miscellaneous Math 2020-09-16, 13:56
Replies: 35
Views: 1,067
Posted By Dr Sardonicus
No. This isn't what your paper says (it does...

No. This isn't what your paper says (it does give a result about the off-diagonal entry of Ap however). The trace polynomials are monic, with constant terms given by Lucas numbers. For prime...
Forum: Soap Box 2020-09-16, 01:06
Replies: 29
Views: 1,305
Posted By Dr Sardonicus
I assume you served in Vietnam. I assume you...

I assume you served in Vietnam. I assume you were not a policy maker.

I suppose you could have chosen to write yourself a ticket to Leavenworth by refusing to be drafted, or gotten an...
Forum: Lounge 2020-09-15, 15:36
Replies: 1,071
Views: 46,282
Posted By Dr Sardonicus
Well, as long as it's mostly old people, who...

Well, as long as it's mostly old people, who cares? Their lives obviously aren't sacred.

I think it was one of the "Feiffer's fables" cartoons back in the day, with the conclusion, "The pre-born...
Forum: Lounge 2020-09-15, 12:24
Replies: 1,071
Views: 46,282
Posted By Dr Sardonicus
:tantrum: Just a pedantic nitpick, perhaps,...

:tantrum:

Just a pedantic nitpick, perhaps, but what you describe is not a Hobson's choice. I think it is more properly described as a dilemma.

A Hobson's choice is a "take it or leave it"...
Forum: Lounge 2020-09-15, 12:13
Replies: 1,071
Views: 46,282
Posted By Dr Sardonicus
I would point out that this also ascribes...

I would point out that this also ascribes motives. That is worrisome enough.

But it also dismisses out of hand the idea that the "lockdown" measures were put in place and remain in place because...
Forum: Lounge 2020-09-15, 11:27
Replies: 42
Views: 1,678
Posted By Dr Sardonicus
Nice shot. Looks like a Southern species of...

Nice shot.

Looks like a Southern species of walkingstick (Anisomorpha). Similar picture at Bugguide here (https://bugguide.net/node/view/1705880/bgimage).

Some insects fly around while they're...
Forum: Lounge 2020-09-14, 13:55
Replies: 1,002
Views: 43,068
Posted By Dr Sardonicus
I don't have a problem with that. Energy has...

I don't have a problem with that. Energy has mass. Of course, the energy that goes into the capacitor or into heating something has to come out of something else, and that something else will...
Forum: Hardware 2020-09-14, 13:23
Replies: 9
Views: 462
Posted By Dr Sardonicus
Looks like it's a done deal. ARM: UK-based...

Looks like it's a done deal.

ARM: UK-based chip designer sold to US firm Nvidia (https://www.bbc.co.uk/news/technology-54142567)
Forum: Miscellaneous Math 2020-09-14, 13:16
Replies: 8
Views: 309
Posted By Dr Sardonicus
If p is prime then 2p - 2 is divisible by 2p. So...

If p is prime then 2p - 2 is divisible by 2p. So if q divides 2p - 1, gcd(q-1, 2p - 2) is divisible by 2p.

However, 2n - 2 is divisible by 2 but not by 4 if n > 1. If p is prime and the...
Forum: Soap Box 2020-09-14, 12:51
Replies: 29
Views: 1,305
Posted By Dr Sardonicus
Yes, it's almost certainly true that just about...

Yes, it's almost certainly true that just about all the folks who worship are in thrall to support the incumbent are immune to argumentation. And I doubt many people who can't stand the incumbent...
Forum: Soap Box 2020-09-13, 13:51
Replies: 29
Views: 1,305
Posted By Dr Sardonicus
2 California deputies shot in apparent ambush in...

2 California deputies shot in apparent ambush in patrol car (https://apnews.com/ef8c6c26b42c53d092645bb054060379)If these "protesters" want the current occupant of the White House re-elected, they...
Forum: Probability & Probabilistic Number Theory 2020-09-13, 13:39
Replies: 2
Views: 2,952
Posted By Dr Sardonicus
I'd been meaning to look at this for a while. I...

I'd been meaning to look at this for a while. I finally got around to it.

In the present situation, we want p and q = 2*k*p + 1 both to be prime. The Bateman-Horn Conjecture says there is a...
Forum: Lounge 2020-09-12, 21:50
Replies: 1,488
RIP
Views: 97,048
Posted By Dr Sardonicus
John Steed and and Emma Peel were such popular...

John Steed and and Emma Peel were such popular characters, they were parodied in contemporary TV series.

The episode "Run, Robot, Run" (first aired 16 March 1968) in Get Smart featured an obvious...
Forum: Miscellaneous Math 2020-09-12, 21:33
Replies: 3
Views: 169
Posted By Dr Sardonicus
I question the use of the term "conjecture,"...

I question the use of the term "conjecture," which, as explained here (https://www.mersenneforum.org/showpost.php?p=554339&postcount=15), implies the statement is important and worthy of study. The...
Forum: Miscellaneous Math 2020-09-12, 20:05
Replies: 35
Views: 1,067
Posted By Dr Sardonicus
I did notice one unusual situation: The...

I did notice one unusual situation:

The characteristic polynomial is x^2 - (u + 1)*x + (u - 1); the discriminant is u^2 - 2*u + 5. As long as this is nonzero (mod p), there are two eigenvalues,...
Forum: Lounge 2020-09-12, 01:50
Replies: 42
Views: 1,678
Posted By Dr Sardonicus
Reminds me of Waldo <shudder>. (taps fist on...

Reminds me of Waldo <shudder>.

(taps fist on head) Here's knocking on wood, hoping that what's raining down doesn't eliminate the whole neighborhood.

The year after the Waldo Canyon Fire, the...
Forum: Miscellaneous Math 2020-09-12, 01:09
Replies: 8
Views: 329
Posted By Dr Sardonicus
First example: Taking n = 1, f = 1 divides 2p - 1...

First example: Taking n = 1, f = 1 divides 2p - 1 for any p.

First example with prime f: p = 3, n = 2; f = 2*22 - 1 = 7 divides 23 - 1 = 7.

Second example with prime f: p = 5, n = 4; f = 2*42 -...
Forum: Factoring 2020-09-11, 13:22
Replies: 12
Views: 540
Posted By Dr Sardonicus
Exactly three versus exactly two prime factors,...

Exactly three versus exactly two prime factors, not sure. Exactly two versus more than two, long-known data suggest "no contest."

I'll assume, for the sake of discussion, that you mean Mersenne...
Forum: Lounge 2020-09-11, 01:15
Replies: 42
Views: 1,678
Posted By Dr Sardonicus
This is one of the Monarch caterpillars on my...

This is one of the Monarch caterpillars on my milkweed. I hadn't seen any of them out in the open lately, but today there were a bunch of them in plain sight. A better insect photographer than I...
Forum: Lounge 2020-09-11, 01:12
Replies: 42
Views: 1,678
Posted By Dr Sardonicus
I will pass this on. It's been many years since...

I will pass this on. It's been many years since I gave up my two mugs of morning coffee because my stomach started complaining. I still enjoy an occasional cup of good coffee as a treat, though.
...
Showing results 1 to 25 of 1000

 
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