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The filtering function is equivalent to noDivsBy defined as part of isPrime function , except that the comparisons testing for the square root are no longer needed and so are spared.
Note that this is a filter - it selects values from its argument which are prime. If no suitable values are found the resulting sequence of primes will be empty.
See also: Sieve of Eratosthenes. I've chosen to solve this task by creating a new iterator type, TDPrimes.
TDPrimes contains the upper limit of the sequence. The iteration state is the list of computed primes, and the item returned with each iteration is the current prime.
The core of the solution is the next method for TDPrimes , which computes the next prime by trial division of the previously determined primes contained in the iteration state.
More to see in . Using the basic prime function from: "Primality by trial division". This example uses infinite lists streams to implement a sieve algorithm that produces all prime numbers.
Since a prime's multiples that count start from its square, we should only add them when we reach that square. Same algorithm as above, but now using threads and channels to produce a channel of all prime numbers similar to newsqueak.
The macro at the top is a convenient wrapper around definitions of channels using a thread that feeds them.
This is an open-ended approach and it's a simple implementation and could be optimized more with some easy programming. The Prime class in the standard library has several Prime generators.
In some methods it can be specified which generator will be used. The generator can be used on it's own:. Using Streams, the "unfaithful sieve" , i.
The above code is extremely inefficient for larger ranges, both because it tests for primality using computationally expensive divide modulo operations and because it sets up deferred tests for division by all of the primes up to each prime candidate, meaning that it has approximately a square law computational complexity with range.
This example uses totally naive looping over test divisors d of n up to n-1 until a divisor is found or the range is exhausted.
As we're generating a sequence of primes, we can use that sequence of primes to describe what we're filtering against.
The code in Extensible prime generator zkl is a much better solution to this problem. The Method filter1 stops at the first non False result, which, if there is one, is the first found diviser, thus short cutting the rest of the test.
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