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Search: Posts Made By: Dr Sardonicus
Forum: Lounge 2021-11-30, 22:40
Replies: 273
Views: 34,340
Posted By Dr Sardonicus
And they decided to celebrate in style! ...

And they decided to celebrate in style!

Barbados bids farewell to British monarchy, becomes republic...
Forum: Lounge 2021-11-30, 17:54
Replies: 1,528
Views: 160,920
Posted By Dr Sardonicus
Three weeks ago, the Great State of Colorado...

Three weeks ago, the Great State of Colorado activated Crisis Standards of Care for hospital staffing statewide. Here's an update. I noticed something bearing on the current line of discussion. (my...
Forum: And now for something completely different 2021-11-30, 16:22
Replies: 14
Views: 7,527
Posted By Dr Sardonicus
It occurred to me to wonder how likely it might...

It occurred to me to wonder how likely it might be that an L-digit block of decimal digits of Mp is prime. I'll assume that L is large enough to make it interesting, but small compared to the number...
Forum: Lounge 2021-11-30, 14:25
Replies: 4,402
Views: 376,488
Posted By Dr Sardonicus
Apparently Lenin had a reputation as quite the...

Apparently Lenin had a reputation as quite the orator. I heard attributed to one of the old Bolsheviks which was, as best I can recall: "When Trotsky spoke, we stood enthralled. When Lenin spoke -...
Forum: Number Theory Discussion Group 2021-11-30, 13:53
Replies: 15
Views: 664
Posted By Dr Sardonicus
Not AFAIK. Probably better to ask whether any...

Not AFAIK. Probably better to ask whether any Mersenne numbers are Carmichael numbers. I will here restrict this question to prime exponents, since Mn has algebraic factors so is obviously...
Forum: And now for something completely different 2021-11-30, 03:16
Replies: 14
Views: 7,527
Posted By Dr Sardonicus
I get Gleitkomma = floating point; Rechner =...

I get

Gleitkomma = floating point; Rechner = computer; Heizgerät = heating device

The word for computer sounds very close to "reckoner." I like that!

I'm not sure how the results are being...
Forum: MattcAnderson 2021-11-30, 00:14
Replies: 9
Views: 181
Posted By Dr Sardonicus
I challenge you to justify this statement. ...

I challenge you to justify this statement. Bronze is not an element. The term "metal," though applicable especially to metallic elements, is also generally applicable to any substance that has the...
Forum: Lounge 2021-11-29, 20:17
Replies: 1,528
Views: 160,920
Posted By Dr Sardonicus
This line of discussion may bear on the disparity...

This line of discussion may bear on the disparity in case-fatality ratios in different countries. I'm not willing to chalk it all up to variations in detection and the reporting process.

One...
Forum: Information & Answers 2021-11-29, 19:52
Replies: 17
Views: 1,071
Posted By Dr Sardonicus
In the spirit of "20 is an arbitrary parameter,"...

In the spirit of "20 is an arbitrary parameter," the following mindless script looks for a triple p, p + 2, p + k which are consecutive primes, for even integers k > 2 which are not congruent to 1...
Forum: Homework Help 2021-11-29, 16:05
Replies: 23
Views: 4,067
Posted By Dr Sardonicus
Of course! And for 0 < k < p,...

Of course! And for 0 < k < p, \frac{p!}{k!(p-k)!} clearly is divisible by p because the denominator is composed of factors less than p.

The result can be extended slightly. Since p divides...
Forum: FermatSearch 2021-11-29, 14:43
Replies: 345
Views: 82,529
Posted By Dr Sardonicus
Thanks for posting the news! From the Fermat...

Thanks for posting the news!

From the Fermat Search News page (http://www.fermatsearch.org/news.html):
Forum: Information & Answers 2021-11-29, 13:51
Replies: 17
Views: 1,071
Posted By Dr Sardonicus
Just to make the list a bit more exclusive, I...

Just to make the list a bit more exclusive, I told Pari-GP to look for primes p such that p + 2 and p + 18 were the next two consecutive primes. With the small limit I chose, it would have taken...
Forum: MattcAnderson 2021-11-29, 13:39
Replies: 9
Views: 181
Posted By Dr Sardonicus
It seems there is a sequence of "metallic ratios"...

It seems there is a sequence of "metallic ratios" or metallic means (https://everything.explained.today/Metallic_mean/), the nth being given by the simple continued fraction [n;n,n,n,n,...] which...
Forum: Miscellaneous Math 2021-11-29, 13:21
Replies: 429
Views: 39,946
Posted By Dr Sardonicus
If only you had found long beforehand the...

If only you had found long beforehand the "symbolic exponents" indicating the "hidden" Mersenne prime exponents from 1398269 to 82589933 were close by!

Think - just think! how far the work of...
Forum: And now for something completely different 2021-11-29, 02:30
Replies: 14
Views: 7,527
Posted By Dr Sardonicus
OK, number of digits in Mp, indicated blocks of...

OK, number of digits in Mp, indicated blocks of indicated number of decimal digits extracted from Mp which represent primes - or at least PRPs - looks right.

I suspect that all or most of the...
Forum: And now for something completely different 2021-11-28, 19:53
Replies: 14
Views: 7,527
Posted By Dr Sardonicus
The first two entries are n, p where p is the...

The first two entries are n, p where p is the exponent of the nth (known) Mersenne prime. I don't know what "MV," "SB," or "AH" signify.

I fed the expression (2^89/10^2)%10^21 to Pari-GP and got...
Forum: Lounge 2021-11-28, 16:10
Replies: 1,528
Views: 160,920
Posted By Dr Sardonicus
Well, sort of. The exact 1918 "Spanish flu"...

Well, sort of. The exact 1918 "Spanish flu" isn't circulating, but direct descendants certainly have been ever since. I became personally acquainted with one of them, the 1968 "Hong Kong flu."
...
Forum: Miscellaneous Math 2021-11-28, 15:34
Replies: 429
Views: 39,946
Posted By Dr Sardonicus
What might be interesting, or at least...

What might be interesting, or at least illustrative, would be to compare the actual amount of computing (GHz hours) required for the CERT compared to that for the PRP test. I can't compare elapsed...
Forum: Lounge 2021-11-28, 14:48
Replies: 1,528
Views: 160,920
Posted By Dr Sardonicus
This CNN story...

This CNN story (https://www.cnn.com/2021/11/28/health/us-coronavirus-sunday/index.html) has some interesting quotations.
Forum: Homework Help 2021-11-27, 15:16
Replies: 23
Views: 4,067
Posted By Dr Sardonicus
Clearly binomial(p-1,0) = 1 = (-1)^0, so it's...

Clearly binomial(p-1,0) = 1 = (-1)^0, so it's true for k = 0. Simplify the ratio binomial(p-1,k+1)/binomial(p-1,k) [you wind up with one linear term in the numerator and one in the denominator]. ...
Forum: Lounge 2021-11-27, 13:38
Replies: 1,808
RIP
Views: 188,887
Posted By Dr Sardonicus
Stephen Sondheim...

Stephen Sondheim (https://www.bbc.com/news/entertainment-arts-52125017)
Forum: Lounge 2021-11-27, 03:48
Replies: 1,528
Views: 160,920
Posted By Dr Sardonicus
Curiously, Africa heretofore seems to have had a...

Curiously, Africa heretofore seems to have had a fairly low incidence of COVID-19 despite low vaccination rates.

Now, a new variant shows up in southern Africa - and elsewhere.

Are people...
Forum: Lounge 2021-11-26, 19:10
Replies: 54
Views: 5,832
Posted By Dr Sardonicus
"Under a low grill?" Broil on low, perhaps? ...

"Under a low grill?" Broil on low, perhaps?

Do you mean Vade retro Satana ?
Forum: Lounge 2021-11-26, 18:47
Replies: 54
Views: 5,832
Posted By Dr Sardonicus
Southern Corn Pudding Based on the recipe in...

Southern Corn Pudding

Based on the recipe in my mom's old Fannie Farmer cookbook

You will need

A buttered casserole dish of 3-pint capacity, and a pan big enough to hold the casserole dish...
Forum: Lounge 2021-11-26, 15:50
Replies: 54
Views: 5,832
Posted By Dr Sardonicus
All I can figure is, you've never had the real...

All I can figure is, you've never had the real deal.

Make no mistake, I've eaten my share of the boxed or Velveeta-based travesties alternatives, and would do so again in a pinch. God help me, I...
Showing results 1 to 25 of 1000

 
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