What's the best algorithm to check if a number is prime?
The answer really depends on a lot of factors.First of all, the size. For small numbers, the division test works pretty well. Check for all numbers up to [math]\sqrt n[/math] for division. If a lot of such numbers need to be tested for primality, some sieving algorithm can be used to find the primality of the entire range.For large [math]n[/math], this method starts being too slow. So we need to look for something better. Here, we need to make an important decision. What do we mean by checking whether a number is prime? Will an answer which is correct with an extremely high probablility do? This is because the probabilistic algorithms for checking primality are much faster than the deterministic ones. A good, fast example of a probabilistic algorithm is Miller–Rabin primality test, which gives an answer with only a [math]4^{-k}[/math] probability of being wrong when [math]k[/math] potential compositeness witnesses are used. Such algorithms are enough for real life applications.Now if you really really need a deterministic algorithm, go for Elliptic curve primality proving or AKS primality test. They are way slower than the probabilistic algorithms, but still polynomial time and hence faster than all the brute force methods.Also, if you know that your number has some special form, there are specialised algorithms which are faster. These are Lucas–Lehmer primality test (for Mersenne numbers : numbers of the form [math]2^{p}-1[/math]), Lucas–Lehmer–Riesel test (for numbers of the form [math]k 2^{n}-1[/math]), Pépin's test (for Fermat numbers : numbers of the form [math]2^{2^n} + 1[/math]).
Why is an eclipse season some 31-37 days long?
As you know there is not every month an eclipse because the moon orbit is tilted. So only when the Full or New Moon is close to her ascending or descending 'nodes' along her orbit, a Solar Eclipse or a Lunar Eclipse happens. Keep in mind one counts eclipses in the dimmer sideway shadow (penumbra) as well. And the eclipse happens for someone on Earth, so it's possible you have to travel. So, an "eclipse season" is a time interval in which the moon is close enough to her nodes when she is Full and New. So during such 'season' an eclipse will occur, but the nice thing is now that it can be two times after each other (e.g. a solar and lunar eclipse), or even three times after each other (e.g. lunar, solar, and lunar again, since the penumbra counts as well). So always half a month between them. So the eclipse season is the period in which eclipses can occur after each other. You can also say such eclipse seasons happen every half year (Full and New moons are close to the nodes every half year).
How likely is it that the Earth is actually not round?
Actually it is an oblate spheroid (a little fatter in the middle).But to answer your question:0.00000000000000000000000000000000000000000000000000000000000000000000000000000%You can watch the world going by from the International Space Station.You can even download an app that tells you when it is overhead so you can go out and if the sun is in the right place you can see it going over while you watch the live images on your smartphone.If that is too hard, here is a picture I took from Concorde in 1999 at Mach 2.0 and 60,000′.You can easily see the curvature of the Earth.Enjoy!
How different is Nowruz in the present in Iran compared to the past?
Nowruz faded into relative non-existence in most areas of Iran following the Islamic conquest, other than rural areas where Zoroastrian villagers kept the festival alive. However after several centuries of suppression, Iranian dynasties started celebrating the festival as an event.However it was not until the rise of Reza Shah and the overthrow of the extremely Arabistic Qajar Dynasty that Nowruz was popularized and revived fully, with the popularization of Chaharshanbe Suri and Sizdabedar.You could also compare it to pre-Islamic Iran, where it would be a significantly more religious festival and people would celebrate the day with the ancient traditions, however most of that tradition has been lost due to Islamization of Iran.
How do I get 0-100 prime numbers (source code) in Java?
What you can do is creating two for loops, one from 1-100, the other one from 1 to the current number. Then you take the remainder of (current number / the loop), if the remainder is 0 and the loop isn't (1 or the current number) then it's not prime.Another way is that you can have a temp variable where add the total numbers which returns remainder of 0. If that variable if more than 2 then it is not prime and vice versa. (The code below follows this explanation)for(int i=1; i <= 100; i++) { int tot = 0; for(int x=1; x<=i; x++) { if(i%x==0){ tot ++; } } if(tot <= 2) System.out.println(i);}Hope that was clear.Good luckUPDATESorry, wrote the code in a hurry. Now it works fine.