===== Prime enumeration =====
==== Function ====

| @#FF9944: definition  | @#FF9944: $p : {\mathbb N}_+\to{\mathbb P}$ |
| @#FF9944: definition  | @#FF9944: $p(1):=2$ |
| @#FF9944: definition  | @#FF9944: $p(n+1):={\mathrm{min}}({\mathbb P}\setminus{X_n})$ |
| @#BBDDEE: with        | @#BBDDEE: $X_n\equiv\{m\in{\mathbb P}\mid m\le p(n)\}$ | 

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=== Code ===
<code haskell>
primes0 :: [Integer]
primes0 = filter prime0 [2..]    

prime0 :: Integer -> Bool
prime0 n | n < 1     = error "not a positive integer"
         | n == 1    = False 
         | otherwise = ld n == n
</code>

using [[Least divisor function]]:
<code haskell>
divides :: Integral a => a -> a -> Bool
divides d n = rem n d == 0

ld :: Integral a => a -> a
ld n = ldf 2 n
 
ldf :: Integral a => a -> a -> a
ldf k n | divides k n = k 
      	| k^2 > n     = n
	| otherwise   = ldf (k+1) n
</code>

using [[Set of divisors function]]:
<code haskell>
divides :: Integral a => a -> a -> Bool
divides d n = rem n d == 0
</code>

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=== Element of ===
[[Bijective function]]
=== Requirements ===
[[Prime number]]
=== Code reference ===
[[Least divisor function]]