feat(euler): Optimize problem 034 with a lower upper bound

ArnabTechiee · ArnabTechiee · commit beda6fc69abc · 2025-10-16T17:20:46.000+05:30
diff --git a/project_euler/problem_034/sol1.py b/project_euler/problem_034/sol1.py
@@ -30,7 +30,9 @@ def solution() -> int:
     >>> solution()
     40730
     """
-    limit = 7 * factorial(9) + 1
+    # The upper bound is 1,499,999, as shown in this proof:
+    # https://math.stackexchange.com/a/112383/89462
+    limit = 1_499_999
     return sum(i for i in range(3, limit) if sum_of_digit_factorial(i) == i)
 
 

Original file line number	Diff line number	Diff line change
`@@ -30,7 +30,9 @@ def solution() -> int:`
`30`	`30`	`>>> solution()`
`31`	`31`	`40730`
`32`	`32`	`"""`
`33`		`- limit = 7 * factorial(9) + 1`
	`33`	`+ # The upper bound is 1,499,999, as shown in this proof:`
	`34`	`+ # https://math.stackexchange.com/a/112383/89462`
	`35`	`+ limit = 1_499_999`
`34`	`36`	`return sum(i for i in range(3, limit) if sum_of_digit_factorial(i) == i)`
`35`	`37`
`36`	`38`