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⎕CR 'PrimeNumbers' ⍝ Show APL user-function PrimeNumbers Primes ← PrimeNumbers N ⍝ Function takes one right arg N (e.g., show prime numbers for 1 ... int N) Primes ← (2 =+ ⌿ 0 = (⍳ N) ∘. |⍳ N) / ⍳ N ⍝ The Ken Iverson one-liner PrimeNumbers 100 ⍝ Show all prime numbers from 1 to 100 2 3 5 7 11 13 17 19 23 29 31 37 41 43 ...
Cython also facilitates wrapping independent C or C++ code into python-importable modules. Cython is written in Python and C and works on Windows, macOS, and Linux, producing C source files compatible with CPython 2.6, 2.7, and 3.3 and later versions. The Cython source code that Cython compiles (to C) can use both Python 2 and Python 3 syntax ...
SymPy is an open-source Python library for symbolic computation.It provides computer algebra capabilities either as a standalone application, as a library to other applications, or live on the web as SymPy Live [2] or SymPy Gamma. [3]
The isPrime function was inaccurate, as range doesn't include the higher end, so e.g. if checking for primality of 9, it would try numbers from 2 to 2, and conclude it was prime. I've added 1 to the upper end of the range so that the isPrime function works, in case anyone else comes along and tries to use it.
APL (named after the book A Programming Language) [3] is a programming language developed in the 1960s by Kenneth E. Iverson. Its central datatype is the multidimensional array. It uses a large range of special graphic symbols [4] to represent most functions and operators, leading to
A built-in function, or builtin function, or intrinsic function, is a function for which the compiler generates code at compile time or provides in a way other than for other functions. [23] A built-in function does not need to be defined like other functions since it is built in to the programming language.
The program is run by updating the integer n as follows: for the first fraction f in the list for which nf is an integer, replace n by nf; repeat this rule until no fraction in the list produces an integer when multiplied by n, then halt. Conway 1987 gives the following FRACTRAN program, called PRIMEGAME, which finds successive prime numbers:
A prime sieve or prime number sieve is a fast type of algorithm for finding primes. There are many prime sieves. The simple sieve of Eratosthenes (250s BCE), the sieve of Sundaram (1934), the still faster but more complicated sieve of Atkin [1] (2003), sieve of Pritchard (1979), and various wheel sieves [2] are most common.