Enter a number to check if it is a Hilbert number, or enter a start and end value to generate all Hilbert numbers within the range.
Hilbert Number Check or Generate
Result
Result
What Is a Hilbert Number?
A Hilbert number is a positive integer in the form \(4n + 1\), where \(n\) is a non-negative integer. Examples of Hilbert numbers include: 1, 5, 9, 13, 17, and so on.
How to Determine if a Number Is a Hilbert Number
To check whether a given number \(x\) is a Hilbert number:
Subtract 1 from \(x\).
Check if the result is divisible by 4. If \((x - 1) \mod 4 = 0\), then \(x\) is a Hilbert number. Otherwise, \(x\) is not a Hilbert number.
Examples
Example 1: Check if 141 is a Hilbert number
Solution:
1. Subtract 1 from \(x\):
\(141 - 1 = 140\).
2. Check divisibility by 4:
\(140 \div 4 = 35\), which is an integer.
Result: 141 is a Hilbert number because it satisfies the \(4n + 1\) form.
Example 2: Check if 12 is a Hilbert number
Solution:
1. Subtract 1 from \(x\):
\(12 - 1 = 11\).
2. Check divisibility by 4:
\(11 \div 4 = 2\) remainder \(3\), so 11 is not divisible by 4.
Result: 12 is not a Hilbert number because it does not satisfy the \(4n + 1\) form.