What is the 145th prime number?
The 145th prime number is 829. The next prime is 839 (a gap of 10) and the one before is 827.
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 145th one is 829.
- 2
829 is prime because no prime up to ā829 ā 28.79 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 145th prime is close to 145 Ć ln(145) ā 722, and here it is 829.
- 4
829 is a twin prime: 827 and 829 are both prime.
Primes around the 145th
| Position | Prime | Gap from the previous |
|---|---|---|
| 142 | 821 | 10 |
| 143 | 823 | 2 |
| 144 | 827 | 4 |
| 145 | 829 | 2 |
| 146 | 839 | 10 |
| 147 | 853 | 14 |
| 148 | 857 | 4 |
Questions
What is the 145th prime number?
829.
Which prime number is 829?
829 is the 145th prime number.
What is the sum of the first 145 primes?
54,998.