tompng · July 27, 2025 14:16 · Jul 27, 2025
diff --git a/manyzero.rb b/manyzero.rb
@@ -0,0 +1,31 @@
+def euclidsolve(cx, cy, c, small)
+  return euclidsolve(cy, cx, c, small).reverse if cx > cy
+  # cx <= cy
+  # x * cx + y * cy = c + small
+  # p [cx.to_f, cy.to_f, c.to_f, small.to_f]
+  if small >= cy
+    # cx <= cy, c < cy
+    # cx*x + cy*y == c + small
+    # x=0; cy*y == c + small
+    return [0, 1]
+  end
+  x, y = euclidsolve(cx, cy % cx, c % cx, small)
+  # x * cx + y * (cy%cx) == c%cx + small
+  #   (x+dx) * cx + (y+dy) * (cy%cx + (cy/cx)*cx) == c%cx + (c/cx)*cx + small
+  #   dx * cx + dy  + (y+dy) * (cy/cx)*cx == (c/cx)*cx
+  [x + (c/cx) - y * (cy/cx), y]
+end
+
+x,y=euclidsolve(cx=2**622, cy=10**187, c=10**(187-16)/2, small=2**(621-53))
+(53..1024).each do |bit|
+  exp10 = (-400..400).bsearch{
+    2**bit<10**it
+  }-1
+  x,y=euclidsolve(cx=2**bit, cy=10**exp10, c=10**(exp10-16)/2, small=2**(bit-1-53))
+  if x.abs.bit_length <= 53
+    f=(x*2**bit)
+    match = f.to_s[/^\d{14}+0{5,}+[1-9]|^\d{14}9{5,}+[0-8]/]
+    p [match.size, match, f.to_f] if match && match.size > 16
+  end
+rescue
+end