From fda3a488084522acc9bff0815a42457b96ff99b3 Mon Sep 17 00:00:00 2001
From: Flancian <0@flancia.org>
Date: Thu, 11 May 2023 22:14:58 +0200
Subject: [PATCH] autopushed

---
 406.md | 19 +++++++++++++------
 1 file changed, 13 insertions(+), 6 deletions(-)

diff --git a/406.md b/406.md
index 1136027b5..515be5112 100644
--- a/406.md
+++ b/406.md
@@ -1,6 +1,13 @@
-- Significantly harder to factor than [[405]], which I find interesting.
-- I think the fact that 405 and 406 are adjacent in the number line and have wildly differing difficulties of factorization probably says something about the nature of numbers? analyzing this fact can probably lead to interesting relations
-- [[203]] * 2 but then I'm stumped, 203 could be a prime. I hope it is, maybe?
-- It's clearly not divisible by 3 if you already checked [[406]] (sum of digits 10, not divisible by 3), but I still checked out of custom. While doing this, remembering which numbers you don't have to check is useful as it prevents duplicate work. Still I'm not concerned about repeating checks because I enjoy them.
-- There is a bound for possible divisors we have to check; the bound is the square root of 203. That means that we may have gained some equity by not having taken the square root of 406, potentially harder to calculate than that of 203.
-- In this case, though, the square root of 400 comes easier (to me): 20.
+- a [[number]].
+  - Significantly harder to factor than [[405]], which I find interesting.
+  - I think the fact that 405 and 406 are adjacent in the number line and have wildly differing difficulties of factorization probably says something about the nature of numbers? analyzing this fact can probably lead to interesting relations
+  - [[203]] * 2 but then I'm stumped, 203 could be a prime. I hope it is, maybe?
+  - It's clearly not divisible by 3 if you already checked [[406]] (sum of digits 10, not divisible by 3), but I still checked out of custom. While doing this, remembering which numbers you don't have to check is useful as it prevents duplicate work. Still I'm not concerned about repeating checks because I enjoy them.
+  - There is a bound for possible divisors we have to check; the bound is the square root of 203. That means that we may have gained some equity by not having taken the square root of 406, potentially harder to calculate than that of 203.
+  - In this case, though, the square root of 400 comes easier (to me): 20.
+  - But because we need to check divisors, we'll want the tighter bound. 203 can't be divisible by 5, can it be divisible by 7?
+  - 7 * 17 is 119, I know because they are my favourite numbers -- is this useful? It tells me that in 7 * [[x]] X is bound to be lower than 34.
+  - 210 which is nearer 203 is clearly 7 * 30 because 21 is 7 * 3.
+  - And lo and behold, 210-203 is 7 :) So we got our answer:
+  - [[406]] is [[2]] * [[7]] * [[29]]
+  - Beautiful!