What is the 142nd prime number?
The 142nd prime number is 821. The next prime is 823 (a gap of 2) and the one before is 811.
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 142nd one is 821.
- 2
821 is prime because no prime up to ā821 ā 28.65 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 142nd prime is close to 142 Ć ln(142) ā 704, and here it is 821.
- 4
821 is a twin prime: 821 and 823 are both prime.
Primes around the 142nd
| Position | Prime | Gap from the previous |
|---|---|---|
| 139 | 797 | 10 |
| 140 | 809 | 12 |
| 141 | 811 | 2 |
| 142 | 821 | 10 |
| 143 | 823 | 2 |
| 144 | 827 | 4 |
| 145 | 829 | 2 |
Questions
What is the 142nd prime number?
821.
Which prime number is 821?
821 is the 142nd prime number.
What is the sum of the first 142 primes?
52,519.