Divisible by Itself and One: Kae Tempest

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I’ve been on tour for a long time. I’m looking forward to some writing time. I’ve got a new album that is in process, but it won’t be out for some time. I’ve got a novel I’m working on, and a couple more ideas. I’m cooking away. Hopefully I’ll have some exciting stuff for people to hear in the not too distant future. Many people will be reading this on the train or bus on their way to work. Can you add a bit of poetry to their mornings?

The confusion begins with this definition a person might give of “prime”: a prime number is a positive whole number that is only divisible by 1 and itself. The number 1 is divisible by 1, and it’s divisible by itself. But itself and 1 are not two distinct factors. Is 1 prime or not? When I write the definition of prime in an article, I try to remove that ambiguity by saying a prime number has exactly two distinct factors, 1 and itself, or that a prime is a whole number greater than 1 that is only divisible by 1 and itself. But why go to those lengths to exclude 1? In 1585, Flemish mathematician Simon Stevin pointed out that when doing arithmetic in base 10, there is no difference between the digit 1 and any other digits. For all intents and purposes, 1 behaves the way any other magnitude does. Though it was not immediate, this observation eventually led mathematicians to treat 1 as a number, just like any other number. Kim : Absolutely, that’s where all the transactions happen between us, and that’s where we make our money.My mathematical training taught me that the good reason for 1 not being considered prime is the fundamental theorem of arithmetic, which states that every number can be written as a product of primes in exactly one way. If 1 were prime, we would lose that uniqueness. We could write 2 as 1×2, or 1×1×2, or 1 594827×2. Excluding 1 from the primes smooths that out. Test to insure the prime test code does not behave poorly or incorrectly with 1, 0 or any negative value.

The first of these properties is what we might think of as a way to characterize prime numbers, but unfortunately the term for that property is irreducible. The second property is called prime. In the case of positive integers, of course, the same numbers satisfy both properties. But that isn’t true for every interesting set of numbers. A factor is more likely a small value that an large one. Testing small values first is generally far more efficient for non-primes. As an example, let’s look at the set of numbers of the form a+ b√-5, or a+i b√5, where a and b are both integers and i is the square root of -1. If you multiply the numbers 1+√-5 and 1-√-5, you get 6. Of course, you also get 6 if you multiply 2 and 3, which are in this set of numbers as well, with b=0. Each of the numbers 2, 3, 1+√-5, and 1-√-5 cannot be broken down further and written as the product of numbers that are not units. (If you don’t take my word for it, it’s not too difficult to convince yourself.) But the product (1+√-5)(1-√-5) is divisible by 2, and 2 does not divide either 1+√-5 or 1-√-5. (Once again, you can prove it to yourself if you don’t believe me.) So 2 is irreducible, but it is not prime. In this set of numbers, 6 can be factored into irreducible numbers in two different ways.

Possible answer:

My own IsPrime() function, written and based on the deterministic variant of the famous Rabin-Miller algorithm, combined with optimized step brute forcing, giving you one of the fastest prime testing functions out there. __int64 power(int a, int n, int mod) Bobby : Do you know about prime numbers, those unique numbers that only have two different factors? The Portobello Bookshop team couldn't be happier to be bringing Kae Tempest to the Assembly Rooms for a celebration of their new collection, Divisible by Itself and One. Getting to welcome Tempest to the bookshop last August was a highlight for many of the team, as well as those who attended in person and online, and this event will be another not to be missed. During the hour-long event, Tempest will be reading and performing some of their new work from Divisible by Itself and One. If you insist on a brute force method, here is just my optimized brute force IsPrime() function: inline bool IsPrime( int number )

Do not use test_factor * test_factor <= number. It risks signed integer overflow (UB) for large primes. Kae Tempest is a poet. They are also a writer, a lyricist, a performer and a recording artist. They have published plays, poems, a novel and a book-length essay, released albums and toured extensively, selling out shows from Reykjavik to Rio de Janeiro. So, imagine your encryption code was the number 15. Can you think of two prime numbers that multiply to make 15?

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Pedantic: Avoid if (number & 1 == 0) {. It is an incorrect test when number < 0 and encoded with rare ones' complement. Use if (number % 2 == 0) { and trust your compiler to emit good code.

is divisible by the prime numbers 2 and 3. The highest power of 2 that 48 is divisible by is \(16=2 Avoid testing with candidate factors above the square root n and less than n. Such test factors are never factors of n. Not adhering to this makes for slow code. They received Mercury Music Prize nominations for both of the albums Everybody Down and Let Them Eat Chaos, and two Ivor Novello nominations for their song-writing on The Book of Traps and Lessons. They were named a Next Generation Poet in 2014, a once-in-a-decade accolade. Tempest also received the Ted Hughes Award for their long-form narrative poem Brand New Ancients and the Leone D’Argento at the Venice Teatro Biennale for their work as a playwright. Good compilers see nearby number/test_factor and number % test_factor and emit code that computes both for the about the time cost of one. If still concerned, consider div(). WARNING: Algorithm deterministic only for numbers < 4,759,123,141 (unsigned int's max is 4294967296)The article mentions but does not delve into some of the changes in mathematics that helped solidify the definition of prime and excluding 1. Specifically, one important change was the development of sets of numbers beyond the integers that behave somewhat like integers. Taking its bearings - and title - from the prime number, Divisible by Itself and One is concerned, ultimately, with integrity: how to live in honest relationship with oneself and others. Avoid sqrt(n). Weak floating point libraries do not perform this as exactly as we need for this integer problem, possible returning a value just ever so less than an expected whole number. If still interested in a sqrt(), use lround(sqrt(n)) once before the loop. If you need to find all the prime numbers below a number, find all the prime numbers below 1000, look into the Sieve of Eratosthenes. Another favorite of mine. Yet many answers here, not only are worse the O(sqrt(n)), they suffer from undefined behavior (UB) and incorrect functionality.