Prime numbers in Python

It may be surprisingly difficult to find a prime number and divide it by the prime number ... How do you do it with Python?

When I saw the gif of [Eratosthenes Sieve](https://ja.wikipedia.org/wiki/Eratosthenes Sieve) on Wikipedia, I thought it would be possible to do this, so I tried it. By example? With lambda binding.

do = lambda *x : x
switch = lambda x : x[-1]


primes = (
  lambda n : find_primes( range( 2, n + 1 ), ( n + 1 ) ** 0.5, [ ] )
)

find_primes = (
  lambda xs, end_point, ys :
    
    switch(
      xs[0] <= end_point and do( ys.append( xs[0] )
              				, find_primes( remove_fst_multiples( xs ) , end_point, ys )
            				)
      
      or   					do( ys.extend( xs ) 
              				, ys 
            				)
    )
)

remove_fst_multiples = (
  lambda xs : [ x for x in xs if x % xs[0]  ]
)

print primes(100)

Execution result:

[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]

The algorithm is the same as Wikipedia.

primes is a function that just passes values in a nice way. The entity is find_primes.

find_primes is

• With the search list, end condition value and prime number list as arguments
• If the number at the beginning of the search list is less than or equal to the end condition value,
• Add the first value to the prime list
• Call find_primes recursively with a new search list excluding multiples of the start value, an end condition value, and a new prime number list.
• If the start value of the search list exceeds the end condition value,
• Combines the remaining search list with the prime list and returns the prime list.

remove_fst_multiples takes a list and returns a list excluding multiples of the first value of the list.

Try using itertools

I received a comment so I tried using it. However, I don't know what it is, so I googled it and replaced the search list with an iterator for the time being. Please see the comments and other announcements on how to use it properly.

from itertools import count, ifilter, takewhile

do = lambda *x : x
switch = lambda x : x[-1]


primes = ( lambda n : 
  find_primes( 
    takewhile(lambda x : x < n + 1, count(2))
  , ( n + 1 ) ** 0.5
  , [ ] 
  )
)

find_primes = (
  lambda xs, end_point, ys :
    (lambda a = next( xs ) :
      
      switch(
       a <= end_point and do( ys.append( a )
               			, find_primes( remove_multiples( xs, a ) , end_point, ys )
              			)
        
        or   			do( ys.append( a )
                		, ys.extend(list( xs) ) 
               			, ys 
             			)
      )
    )()
)

remove_multiples = (
  lambda xs, a : ifilter(lambda x : x % a , xs )
)

print primes(100)