There are three kinds of people in the world, those who can count and those who can't.
There are 10 types of people in the world, those who can count in binary and those who can't.
There are two kinds of people; those who do the work and those who take the credit. Try to be in the first group; there is less competition there.
there are too kinds of people in this world! those who can spel and thos who cant
There are infinite types of people; those who...
The best primality test that I know is a small program that tests all numbers less than or equal to √x where x is the prime number that you are looking for. When you start testing numbers over 200 digits long then you start to run into the problem of finding a solution in this lifetime. There are other methods for finding prime numbers, like counting by primes to cut down on cycles, but I trust the brute-force all inclusive method and have never really needed to calulate primes greater than 50 digits.
I think there are a few proofs that can give limits to your question as in there are at least x number of primes beween 2 and N that are less than or equal to Q. But I am not sure if that is what you are asking.
There are exactly 25 primes less than 100 about %25 of all numbers from 1-100 are prime.
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
mathsyperson got it. He used the same method that I did, "plug-and-chug". Sometimes that's the best way to solve a problem. I also wrote a program to cycle all combinations of all integers from 1-100,000 and only found one unique solution. Later, I found on the same website that I originally found the problem a proof showing there was a single unique solution.
I said it was easy.
Find three positive whole numbers such that for any two of them, the number one less than their product is divisible by the third number.
This is one of my favorite integer problems. The wording is a little off. I think it should read, "their product is evenly divisible", no fractions. I think there is also a proof that shows there is exactly one solution to this problem. When posting solutions, please post your method as well.
(x × y 1) ÷ z = (int)
(y × z 1) ÷ x = (int)
(z × x 1) ÷ y = (int)
Aphex Twin is not the best party music but he is interesting to listen to. Who has heard "Bouncing Balls" from "Pi" (the movie) sound track? Find someone with a good receiver and some expensive speakers pop in that tune and crank up the volume. When the big ball drops near the end of the song it will shake the entire house.
Eleusis was a mathematician from antiquity. Also Robert Abbott invented a card game and named it Eleusis. Published first in 1959 by Martin Gardner of Scientific American, then republished in 1963 and then finally revised in 1977 as "The New Eleusis". Today you can find it in Mathematics discussions, Computer Science programming, and I also think in some circles of Philosophy. The card game is simple and actually really boring to play with real people. What makes it fascinating to me is that programmers can make bots or automaton programs that predict the future (in a sense). Using mathematics to predict certain outcomes and with increasing precision.
I am very interested in pure math, and math for maths sake. I know (3.1415926535) 10 digits of pi by heart and I like to figure out square roots of primes with the long hand method. I think that there is a primality function that has yet to be discovered. I think that pseudo-primes and relatively prime numbers are really cool. I like cryptography and code breaking. I think that e is over-rated and that phi is great. I own a third edition of Penguins book of curious and interesting number by David Wells (you must buy this book) and a new edition as well. I know C/C++, java, pascal, perl and bits and pieces of other languages.
A reporter asked three specialists to give her the value of Pi:
Mathematician: Pi is exactly the ratio of the circumference of a circle and its diameter.
Programmer: Pi is exactly 3.1415926535 for purposes of precision on most operating systems.
Engineer: Pi is 3
A Meteorologist, an Engineer and a Computer Scientist were driving a Jeep through the desert, when all of a sudden the jeep stopped. All three of them open the hood and make suggestions on how to fix the jeep.
Meteorologist: The Sun is at its peak, the engine cant run because its too hot. We need to wait for the sun to go down and then start up the engine.
Engineer: I dont fully agree with you. Yes the engine is over-heated, but we just need to wait for it to cool down some and then we can start it back up and be on our way.
Computer Scientist: Hey everybody. I have an idea, lets all get back into the jeep, open and close the doors three times and see what happens.
Math Teacher: When taking the integral of this equation you have to remember to keep the negative sign, it makes all the difference in the world.
Why is god like a civil engineer? Because he built the human body and only a civil engineer would build a waste disposal system in the middle of a recreational facility.
What did they call the Midget fortune teller who escaped from Jail?
A small, medium, at large!