Lines Matching defs:prime
2 # = prime.rb
18 # Re-composes a prime factorization and returns the product.
32 # Returns true if +self+ is a prime number, false for a composite.
33 def prime?
34 Prime.prime?(self)
37 # Iterates the given block over all prime numbers.
40 def Integer.each_prime(ubound, &block) # :yields: prime
46 # The set of all prime numbers.
50 # Prime.each(100) do |prime|
51 # p prime #=> 2, 3, 5, 7, 11, ...., 97
67 # Prime.instance.prime?(2) #=> true
68 # Prime.prime?(2) #=> true
72 # A "generator" provides an implementation of enumerating pseudo-prime
74 # Furthermore, it is a external iterator of prime enumeration which is
86 # This sequence is very bad as a pseudo-prime sequence. But this
89 # has many prime factors. e.g. for Prime#prime? .
113 # Iterates the given block over all prime numbers.
120 # prime numbers infinitely if +ubound+ is nil.
122 # Optional. An implementation of pseudo-prime generator.
132 # Calls +block+ once for each prime number, passing the prime as
136 # Upper bound of prime numbers. The iterator stops after
137 # yields all prime numbers p <= +ubound+.
153 # Returns true if +value+ is prime, false for a composite.
158 # +generator+:: optional. A pseudo-prime generator.
159 def prime?(value, generator = Prime::Generator23.new)
169 # Re-composes a prime factorization and returns the product.
173 # pair consists of a prime number -- a prime factor --
183 pd.inject(1){|value, (prime, index)|
184 value *= prime**index
192 # +generator+:: Optional. A pseudo-prime generator.
194 # pseudo-prime number in the ascendent
195 # order. It must generate all prime numbers,
196 # but may generate non prime numbers.
220 for prime in generator
222 while (value1, mod = value.divmod(prime)
228 pv.push [prime, count]
230 break if value1 <= prime
238 # An abstract class for enumerating pseudo-prime numbers.
255 # returns the next pseudo-prime number, and move the internal
275 # Iterates the given block for each prime numbers.
281 prime = succ
282 break last_value if prime > @ubound
283 last_value = block.call(prime)
298 each do |prime|
299 yield prime, obj
323 # a prime table generated by trial division.
342 # This is a pseudo-prime generator, suitable on
347 @prime = 1
355 @prime += @step
358 case @prime
359 when 1; @prime = 2
360 when 2; @prime = 3
361 when 3; @prime = 5; @step = 2
364 return @prime
373 # Internal use. An implementation of prime table by trial division method.
390 # Returns the cached prime numbers.
397 # Returns the +index+th prime number.
402 # Only check for prime factors up to the square root of the potential primes,
412 @primes.push @next_to_check if @primes[2..@ulticheck_index].find {|prime| @next_to_check % prime == 0 }.nil?
414 @primes.push @next_to_check if @primes[2..@ulticheck_index].find {|prime| @next_to_check % prime == 0 }.nil?
432 # bitmap for odd prime numbers less than 256.
434 # * 1 if n is prime,
440 # returns the least odd prime number which is greater than +n+.
492 # Returns the next prime number and forwards internal pointer.
500 # Iterates the given block over all prime numbers. Note that enumeration