What is the 1031st prime number?
The 1031st prime number is 8221. The next prime is 8231 (a gap of 10) and the one before is 8219.
Position
Pick any whole number from 1 to 10,000.
How to work it out
- 1
List the primes in order: 2, 3, 5, 7, 11, 13, ā¦ The 1031st one is 8221.
- 2
8221 is prime because no prime up to ā8221 ā 90.67 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 1031st prime is close to 1031 Ć ln(1031) ā 7153, and here it is 8221.
- 4
8221 is a twin prime: 8219 and 8221 are both prime.
Primes around the 1031st
| Position | Prime | Gap from the previous |
|---|---|---|
| 1028 | 8191 | 12 |
| 1029 | 8209 | 18 |
| 1030 | 8219 | 10 |
| 1031 | 8221 | 2 |
| 1032 | 8231 | 10 |
| 1033 | 8233 | 2 |
| 1034 | 8237 | 4 |
Questions
What is the 1031st prime number?
8221.
Which prime number is 8221?
8221 is the 1031st prime number.
What is the sum of the first 1031 primes?
3,933,290.