The number 88001
88001 is a twin prime (88001 and 88003 are both prime) and the 8544th prime number. Its only divisors are 1 and 88001.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 88001: a twin prime (88001 and 88003 are both prime); the 8544th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
88001 is prime, so its only factors are 1 and 88001. It is the 8544th prime; the next prime is 88003 and the one before is 87991.
- 3
The divisors add up to 88002; without 88001 itself that is 1, so 88001 is deficient (1 is less than 88001). Euler's totient φ(88001) = 88000 numbers up to 88001 share no factor with it.
- 4
The digits of 88001 add up to 17, and repeating that until one digit is left gives the digital root 8. The Collatz sequence (halve if even, else 3n+1) takes 71 steps to reach 1.
88001 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 88002 |
| Euler totient φ(n) | 88000 |
| Square | 7744176001 |
| Cube | 681495232264001 |
| Square root | 296.649625 |
| Digit sum / digital root | 17 / 8 |
| Collatz steps to 1 | 71 |
| Scientific notation | 8.8001 × |
88001 in other forms
| Form | Value |
|---|---|
| In words | eighty-eight thousand and one |
| Binary (base 2) | 10101011111000001 |
| Octal (base 8) | 253701 |
| Hexadecimal (base 16) | 157C1 |
| Base 3 | 11110201022 |
| As time | 88001 seconds = 24 h 26 min 41 s |
Is 88001 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | No (remainder 1) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | No (remainder 2) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | No (remainder 1) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 1) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | No (remainder 5) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 4) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | No (remainder 1) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 8) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 1) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 1) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 5) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 88001 a prime number?
Yes. 88001 is divisible only by 1 and itself.
What are the factors of 88001?
1, 88001.
What is 88001 in binary?
10101011111000001 (hexadecimal 157C1, octal 253701).
What is the square root of 88001?
About 296.6496.
Is 88001 divisible by 3?
No. Its digits add up to 17, which is not a multiple of 3.
What is special about the number 88001?
88001 is a twin prime (88001 and 88003 are both prime); the 8544th prime number; a happy number: repeatedly adding the squares of its digits reaches 1.