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+# rotate 90 deg
+r ← ⍉≡⇌
+
+# create spiral numbers with n rows and cols
+# spiral ? n
+s ← (
+  +1⇡ⁿ2 # create n^2 numbers
+  ⊸(
+    ⊸(-1×2√/↥) # t*2 - 1, where t = sqrt(max(range(n^2))) = n
+    ⌈÷2↙       # create [1 1 2 2 3 ...] until sum is n^2
+  )
+  ⊜□˜▽+1°⊏     # successively take 1, 1, 2, 2, 3, ... until all n^2 numbers taken
+  ⇌/◇(˜⊂r)⍜⊢⍚¤ # combine all taken with rotating array to form spiral
+)
+
+# memoized recursive version of s
+σ ← |1 memo(
+  ⨬(⊂⊸(++1⇡∩/↥⊃△(⊢⊢)) r σ-1
+  | ⋅(¤[1]) # base-case
+  )⊸=1
+)
+
+# generates each diagonal of spiral array
+Σ ← +1\+ +¤[2 4 6]×8 ⇡⌊÷2
+
+# get numbers on diagonal
+d ← ⊜°¤ ↥⊸r⊞=. °⊏
+
+# is_prime(n) ? n
+p ← =1⧻°/×
+
+┌─╴test
+  p ↚ ⊜(⊜⋕⊸≠@\s)⊸≠@\n
+  ⍤⤙≍ s 7 p $ 37 36 35 34 33 32 31
+            $ 38 17 16 15 14 13 30
+            $ 39 18  5  4  3 12 29
+            $ 40 19  6  1  2 11 28
+            $ 41 20  7  8  9 10 27
+            $ 42 21 22 23 24 25 26
+            $ 43 44 45 46 47 48 49
+└─╴
+
+Sol! ← +1×2⧻⍢(+2⟜(÷⊃⧻/+≡p ^0)|⋅(>0.1)) ⊙1
+
+# Sol!(d s) 3 # too slow
+# (σ -1×2) == s
+# Sol!(d σ -1×2) 3 # too slow (too much memory usage)
+# Sol!(⊂˜↯1÷2-1⟜(♭ Σ)) 3 # still too slow
+
+# okay... let's do it mathematically from scratch:
+
+# primes on diagonals/number of elements on diagonals
+# Chance ← ÷-1×2⟜(
+#   ⊃((+5+∩×₄⊃×₂ⁿ₂)⇡
+#   | (+3+⊃×₆(×4ⁿ2))⇡
+#   | (+7+⊃×₁₀(×4ⁿ2))⇡
+#   ) ⌊÷2
+#   /+≡p⊂⊂
+# )
+#
+# ⍢(+2|>0.1 Chance) 3
+
+# that solved it in 4 minutes (with p memoized)... too slow!
+
+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)
+)
+
+# 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)
+
+# that's a 240x speedup, from 4 minutes to 1 second. we can go faster...