In number theorya Woodall number W n is any natural number of the form. Woodall numbers were first studied by Allan J. Cunningham and H. Woodall in inspired by James Cullen 's earlier study of the similarly-defined Cullen numbers.
Woodall numbers that are also prime numbers are called Woodall primes ; the first few exponents n for which the corresponding Woodall numbers W n are prime are 2, 3, 6, 30, 75, 81,… sequence A in the OEIS ; the Woodall primes themselves begin with 7, 23, … sequence A in the OEIS. In Christopher Hooley showed that almost all Cullen numbers are composite. It is an open problem on whether there are infinitely many Woodall primes.
Like Cullen numbers, Woodall numbers have many divisibility properties. For example, leaflet draw get coordinates p is a prime number, then p divides.
From Wikipedia, the free encyclopedia. History [ edit ] Woodall numbers were first studied by Allan J.
Woodall primes [ edit ] Unsolved problem in mathematics : Are there infinitely many Woodall primes? C ; Woodall, H. Recurrence sequences. Mathematical Surveys and Monographs.
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Back to top.Are you a writer or content creator? Then take a look at our Content Creators Program! Join our Discord for more Arknights news and discussions. Additional resources: Arknights Tierlist. The only use for Gems is to pull the gacha. You can do a single pull for every gems and will get you a 10 pull.
You can safely use all of your gems on the banners of your choice without worry as that is their sole purpose: to pull your favorite character. They are a catalyst that can be consumed and turned into either stamina or gems. Each stone can be turned into either full stamina, which scales with your level, or gems. During a new event, you can often get at least 10 of these due to all the new stages that come with an event.
The gems per orb are pitiful compared to the other options. I recommend consuming them for stamina or keeping them for costumes. Stamina depletes incredibly quickly and each Prime grants a scalable, full stamina refresh.
They are the only currency that can be used to buy costumes. Damn nice! There is also a level-up package you can buy for x amount of originite prime stones that will return you gems and additional materials. The deadliest of em all, the most precious of them all, the Lungmen Dollars!
They are the equivalent of gold in other games. Lungmen dollars are used for upgrading your characters, upgrading your base, and eliting your characters. They are primarily obtained through a rotational daily resource mission and the trading sites in the base. They should be spent cautiously as the cost for leveling a character at later levels gets exponentially high.
One run of the Lungmen resource mission gives you a measly 7, dollars and takes 30 stamina. Combined with how little stamina you can use a day and having to upgrade the character to max level before you can even unlock the awakening makes Lungmen dollars deplete in a matter of seconds. Base upgrading can also rapidly consumes blow through your supply. Basically use gems to summon.
These recruits takes Recruit Passes instead of gems. As you can see, you can determine how long you want the recruit to be max is 9 hours.Unfortunately, there is a scarcity of descriptive data on the physical characteristics of Asian soccer players. It was conducted in conjunction with the selection of the Hong Kong team before the Beijing Asian Games.
In all, 24 professional soccer players were selected from a pool of players as subjects for the study. The following means s. On average the physique of Hong Kong soccer players appeared to be smaller and lighter than those found in Europe, which may be one of the key factors that contribute to the lack of success of Hong Kong soccer teams in international competition.
National Center for Biotechnology InformationU. Br J Sports Med. Author information Copyright and License information Disclaimer. Copyright notice. This article has been cited by other articles in PMC. A physiological evaluation of professional soccer players. Isokinetic torque levels for knee extensors and knee flexors in soccer players.
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Applied physiology of soccer. Sports Med. Athlete's heart--a review of its historical assessment and new aspects.Join us now! Forgot Your Password? Forgot your Username?
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Essentials Only Full Version. SSC Member. Congratulations, in more ways than one! Too cool I have 2x HP servers on my terrace all year round, was -5'c outside last week and they just kept crunching with no issues. Congrats on your Primes. It was Stack some plywood up in there.Approximating Irrational Numbers (Duffin-Schaeffer Conjecture) - Numberphile
The Crunchinator.Scholars have maintained that public attitudes often diverge from expert consensus due to ideology-driven motivated reasoning. However, this is not a sufficient explanation for less salient and politically charged questions.
More attention needs to be given to anti-intellectualism—the generalized mistrust of intellectuals and experts. Using data from the General Social Survey and a survey of 3, Americans on Amazon Mechanical Turk, I provide evidence of a strong association between anti-intellectualism and opposition to scientific positions on climate change, nuclear power, GMOs, and water fluoridation, particularly for respondents with higher levels of political interest.
Second, a survey experiment shows that anti-intellectualism moderates the acceptance of expert consensus cues such that respondents with high levels of anti-intellectualism actually increase their opposition to these positions in response. Third, evidence shows anti-intellectualism is connected to populism, a worldview that sees political conflict as primarily between ordinary citizens and a privileged societal elite.
Exposure to randomly assigned populist rhetoric, even that which does not pertain to experts directly, primes anti-intellectual predispositions among respondents in the processing of expert consensus cues. These findings suggest that rising anti-elite rhetoric may make anti-intellectual sentiment more salient in information processing. Most users should sign in with their email address.
Physiological profiles of Hong Kong élite soccer players.
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Volume Oxford Academic. Google Scholar. Select Format Select format. Permissions Icon Permissions. Abstract Scholars have maintained that public attitudes often diverge from expert consensus due to ideology-driven motivated reasoning. All rights reserved. For permissions, please e-mail: journals. Issue Section:. You do not currently have access to this article. Download all slides. Sign in.In mathematicsa Fermat number - named after Pierre de Fermat who first studied them - is a positive integer of the form.
The first few Fermat numbers are:. See below for a complete proof. The Fermat numbers satisfy the following recurrence relations :. Each of these relations can be proved by mathematical induction. From the second equation, we can deduce Goldbach's theorem named after Christian Goldbach : no two Fermat numbers share a common integer factor greater than 1.
Then a divides both. This is a contradictionbecause each Fermat number is clearly odd. Fermat numbers and Fermat primes were first studied by Pierre de Fermat, who conjectured but admitted he could not prove that all Fermat numbers are prime. Indeed, the first five Fermat numbers F 0However, the conjecture was refuted by Leonhard Euler in when he showed that.
Fermat was probably aware of the form of the factors later proved by Euler, so it seems curious why he failed to follow through on the straightforward calculation to find the factor.
However, little is known about Fermat numbers for large n. Therefore, the total expected number of Fermat primes is at most. This argument is not a rigorous proof. For one thing, the argument assumes that Fermat numbers behave " randomly ", yet we have already seen that the factors of Fermat numbers have special properties. This makes the test a fast polynomial-time algorithm. However, Fermat numbers grow so rapidly that only a handful of Fermat numbers can be tested in a reasonable amount of time and space.
Because of the size of Fermat numbers, it is difficult to factorize or even to check primality. The elliptic curve method is a fast method for finding small prime divisors of numbers. Distributed computing project Fermatsearch has successfully found some factors of Fermat numbers.
Yves Gallot's proth. By itself, this makes it easy to prove the primality of the known Fermat primes. As of [update]only F 0 to F 11 have been completely factored. It is possible that the only primes of this form are 3, 5, 17, and 65, Indeed, Boklan and Conway published in a very precise analysis suggesting that the probability of the existence of another Fermat prime is less than one in a billion.
The following factors of Fermat numbers were known before since the '50s, digital computers have helped find more factors :. This is because all strong pseudoprimes to base 2 are also Fermat pseudoprimes - i.
Carl Friedrich Gauss developed the theory of Gaussian periods in his Disquisitiones Arithmeticae and formulated a sufficient condition for the constructibility of regular polygons.
Gauss stated without proof that this condition was also necessarybut never published his proof. A full proof of necessity was given by Pierre Wantzel in The result is known as the Gauss—Wantzel theorem :. Fermat primes are particularly useful in generating pseudo-random sequences of numbers in the range 1 … Nwhere N is a power of 2.
Now multiply this by a number Awhich is greater than the square root of P and is a primitive root modulo P i. Then take the result modulo P.