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 Showing results 1 to 25 of 1000 Search took 0.29 seconds. Search: Posts Made By: Dr Sardonicus
 Forum: Puzzles 2021-12-02, 13:52 Replies: 3 Views: 123 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!
 2021-12-01, 20:29 Replies: 17 Views: 7,718 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: 52 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: 182 Views: 13,624 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: 161,373 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: 278 Views: 34,531 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: 161,373 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...
 2021-11-30, 16:22 Replies: 17 Views: 7,718 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: 376,923 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 -...
 2021-11-30, 13:53 Replies: 15 Views: 720 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...
 2021-11-30, 03:16 Replies: 17 Views: 7,718 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: 201 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: 161,373 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: 1,193 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: 4,184 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 Sticky: New Fermat factors Views: 82,728 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: 1,193 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: 201 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: 430 Views: 40,436 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...
 2021-11-29, 02:30 Replies: 17 Views: 7,718 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...
 2021-11-28, 19:53 Replies: 17 Views: 7,718 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: 161,373 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: 430 Views: 40,436 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: 1,529 Views: 161,373 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: 4,184 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]. ...
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