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Forum: Science & Technology 2021-12-04, 14:53
Replies: 516
Views: 89,228
Posted By Dr Sardonicus
Indonesia volcano: Residents flee as Mt Semeru...

Indonesia volcano: Residents flee as Mt Semeru spews huge ash cloud (https://www.bbc.com/news/world-asia-59532251)
Forum: Prime Gap Searches 2021-12-04, 14:38
Replies: 4
Views: 209
Posted By Dr Sardonicus
I note that for a given x, the sequence of least...

I note that for a given x, the sequence of least primes with all g's \ge x for increasing n (down a given column of the table) is monotone increasing; likewise for a given n and increasing lower...
Forum: Hardware 2021-12-03, 15:55
Replies: 10
Views: 2,566
Posted By Dr Sardonicus
US government sues to block $40 billion...

US government sues to block $40 billion Nvidia-Arm chip deal (https://apnews.com/article/technology-business-lifestyle-europe-united-kingdom-d8d599c15b4f4e14e6f7b3f78d09ef07)
Forum: Puzzles 2021-12-02, 13:52
Replies: 4
Views: 316
Posted By Dr Sardonicus
They need a proofreader! That should be has! ...

They need a proofreader! That should be has!

Leave making typos to me - I make enough for everybody!
Forum: And now for something completely different 2021-12-01, 20:29
Replies: 17
Views: 7,760
Posted By Dr Sardonicus
Really? lift(Mod(2,10^4)^82589933 - 1) =...

Really?

lift(Mod(2,10^4)^82589933 - 1) = 2591
lift(Mod(2,10^6)^82589933 - 1) = 902591
lift(Mod(2,10^73)^82589933 - 1) = 4472526640076912114355308311969487633766457823695074037951210325217902591...
Forum: Miscellaneous Math 2021-12-01, 17:28
Replies: 1
Views: 62
Posted By Dr Sardonicus
It depends on what you're given first. If r...

It depends on what you're given first.

If r = x1 is a Pisot number (an algebraic integer > 1 whose algebraic conjugates x2,... xn all have absolute value less than 1) then for positive integer k,...
Forum: Lounge 2021-12-01, 16:21
Replies: 185
Views: 13,802
Posted By Dr Sardonicus
That depends. A 2-digit day number is sometimes...

That depends. A 2-digit day number is sometimes obligatory for filling in dates on forms (MM/DD/YY). With that convention, 12/11/21 and 12/22/21 are the only ones left standing for this month.
Forum: Lounge 2021-12-01, 13:30
Replies: 1,529
Views: 161,725
Posted By Dr Sardonicus
An FDA panel supports Merck COVID drug in mixed...

An FDA panel supports Merck COVID drug in mixed vote (https://www.npr.org/sections/health-shots/2021/11/30/1060130774/an-fda-panel-supports-merck-covid-drug-in-mixed-vote)
Forum: Lounge 2021-11-30, 22:40
Replies: 279
Views: 34,699
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: 1,529
Views: 161,725
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: 17
Views: 7,760
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: 377,473
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: 779
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: 17
Views: 7,760
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: 10
Views: 233
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: 1,529
Views: 161,725
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: 18
Views: 1,387
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: 24
Views: 4,360
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: 82,939
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: 18
Views: 1,387
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: 10
Views: 233
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: 431
Views: 40,944
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: 17
Views: 7,760
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: 17
Views: 7,760
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: 1,529
Views: 161,725
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."
...
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