# project euler 58

p     ← =1⧻°/×
Sieve ← ▽⊸≡p+2⇡

Primes ← Sieve 37417

# is_prime(n) ? n
# p ← ⨬(=|1)⊸=¯1⊸(⍣⊢¯1▽⤚(=0≡◿) Primes ¤)

NewP ← (
  # get the next three prime candidates (lower right is odd square)
  ⊃((+5+∩×₄⊃×₂ⁿ₂)
  | (+3+⊃×₆(×4ⁿ2))
  | (+7+⊃×₁₀(×4ⁿ2))
  )
  ++∩₃p # count how many are prime (0-3)
)

Sol ← (
  # initial values are:
  # - 5: the amount of numbers so far; 1, 3, 5, 7, 9 (counter for diagonal)
  # - NewP.: = 3, since 3, 5, 7 are prime (counter for primes on diagonal)
  # - 0: current NewP generation. NewP 0 is 3 (see above)
  5 NewP. 0
  ⍢(+4 ⊙+ ⊙⊙(⊸NewP+1) # add 4 for new corners, generate NewP(n+1)
  | >0.1 ÷            # check prime ratio
  )
  # discard number of primes and diagonal values,
  # scale generation up to side length
  # newp gen 0 -> 0*2 + 3 = side length 3
  # newp gen 1 -> 1*2 + 3 = side length 5, ...
  ⋅⋅(+3×2)
)