The number 1031
1031 is a twin prime (1031 and 1033 are both prime) and the 173rd prime number. Its only divisors are 1 and 1031.
Pick any whole number from 1 to 100,000.
How to work it out
- 1
What is special about 1031: a twin prime (1031 and 1033 are both prime); the 173rd prime number.
- 2
1031 is prime, so its only factors are 1 and 1031. It is the 173rd prime; the next prime is 1033 and the one before is 1021.
- 3
The divisors add up to 1032; without 1031 itself that is 1, so 1031 is deficient (1 is less than 1031). Euler's totient φ(1031) = 1030 numbers up to 1031 share no factor with it.
- 4
The digits of 1031 add up to 5, and repeating that until one digit is left gives the digital root 5. The Collatz sequence (halve if even, else 3n+1) takes 36 steps to reach 1.
1031 at a glance
| Property | Value |
|---|---|
| Type | prime |
| Number of divisors | 2 |
| Sum of divisors | 1032 |
| Euler totient φ(n) | 1030 |
| Square | 1062961 |
| Cube | 1095912791 |
| Square root | 32.109189 |
| Digit sum / digital root | 5 / 5 |
| Collatz steps to 1 | 36 |
| Scientific notation | 1.031 × |
1031 in other forms
| Form | Value |
|---|---|
| In words | one thousand and thirty-one |
| Roman numerals | MXXXI |
| Binary (base 2) | 10000000111 |
| Octal (base 8) | 2007 |
| Hexadecimal (base 16) | 407 |
| Base 3 | 1102012 |
| As time | 1031 seconds = 17 min 11 s |
Is 1031 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 3) | 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 2) | 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 7) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | No (remainder 5) | 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 8) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | No (remainder 11) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 1031 a prime number?
Yes. 1031 is divisible only by 1 and itself.
What are the factors of 1031?
1, 1031.
What is 1031 in binary?
10000000111 (hexadecimal 407, octal 2007).
What is the square root of 1031?
About 32.1092.
What is 1031 in Roman numerals?
MXXXI.
Is 1031 divisible by 3?
No. Its digits add up to 5, which is not a multiple of 3.
What is special about the number 1031?
1031 is a twin prime (1031 and 1033 are both prime); the 173rd prime number.