# project euler 46

# bool ? n
IsPrime ← memo(=1⧻°/×)
# [all primes below n] ? n
Primes ← +1⊚≡IsPrime↘1⇡
# [all squares below n] ? n
Squares ← ⍜√(↘1⇡+1⌊)
# check if n can be written as 
# sum of prime and twice square
# bool ? n 
Goldbach ← ±⧻⊚=⟜(
  ⊞+⊃(⍜÷₂Squares)Primes
)
# [all odd composites on [a, b)] ? a b
OddComposites ← ▽¬⊸∊ Primes⟜(
  +1 +⤙(⍜÷₂(⇡⌊) ⌵-) ⊙⍜÷₂⌊
):
# [n subintervals a_b] ? a b n
Subintervals ← ⧈₂/⊂+⟜(×⇡+1⤙(˜÷⌵-))

⊢⊙◌⍢(
  +300.◌
  ⤚(
    Subintervals⊙⊙8
    ⍚/OddComposites⌊
    /◇⊂⍚(▽¬⊸≡Goldbach)
  )
| ¬±⧻
) [] 3