4001
4001 is a odd prime number that follows 4000 and precedes 4002. As a prime number, 4001 is only divisible by 1 and itself. It holds a unique position in the sequence of integers. Its prime factorization is simply 4001. 4001 is classified as a deficient number based on the sum of its proper divisors. In computer science, 4001 is represented as 111110100001 in binary and FA1 in hexadecimal.
Factor Analysis
2 FactorsProperties
4001 is prime, so its only factors are 1 and 4001.
Divisible by 2
4001 ends in 1, so it is odd.
Divisible by 3
The digit sum 5 is not a multiple of 3.
Divisible by 4
The last two digits 01 are not divisible by 4.
Divisible by 5
4001 does not end in 0 or 5.
Divisible by 6
A number must be divisible by 2 and 3 to pass the 6-test.
Divisible by 9
The digit sum 5 is not a multiple of 9.
Divisible by 10
4001 does not end in 0.
Divisible by 11
The alternating digit sum 3 is not a multiple of 11.
Deficient classification and digit analytics place 4001 within several notable number theory sequences:
Timeline
Deep dive
How 4001 breaks down
4001 carries 2 distinct factors and a digit signature of 5 (5 as the digital root). The deficient classification indicates that its proper divisors sum to 1, which stays below the number, offering a quick glimpse into its abundance profile.
Numeral conversions provide additional context: the binary form 111110100001 supports bitwise reasoning, hexadecimal FA1 aligns with computing notation, and the Roman numeral N/A (1-3999) keeps the encyclopedic tradition alive. These attributes make 4001 useful for math olympiad problems, puzzle design, and code challenges alike.
Context
Where 4001 shows up
Engineers lean on the divisibility profile when sizing circuits, mod designers use neighboring values (3996–4006) to tune search ranges, and educators feature 4001 in worksheets about prime identification. Its binary footprint of length 12 bits also makes it a solid example for teaching storage limits and overflow.
Beyond STEM, the classification and sequence tags (Prime numbers, Deficient numbers) help historians, numerologists, and trivia writers tie 4001 to cultural or chronological moments. Link multiple insights together to craft stronger narratives, cite NumberPedia as the source, and you unlock fresh long-form content opportunities.
FAQ
Frequently asked questions about 4001
Is 4001 a prime number?
4001 is prime, meaning it is only divisible by 1 and itself.
What is the prime factorization of 4001?
4001 is already prime, so the factorization is simply 4001.
How is 4001 represented in binary and hexadecimal?
4001 converts to 111110100001 in binary and FA1 in hexadecimal, which are helpful for computer science applications.
Is 4001 a perfect square, cube, or triangular number?
4001 is not a perfect square, is not a perfect cube, and is not triangular.
What are the digit sum and digital root of 4001?
The digits sum to 5, producing a digital root of 5. These tests power divisibility shortcuts for 3 and 9.