What is the 146th prime number?
The 146th prime number is 839. The next prime is 853 (a gap of 14) and the one before is 829.
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 146th one is 839.
- 2
839 is prime because no prime up to ā839 ā 28.97 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 146th prime is close to 146 Ć ln(146) ā 728, and here it is 839.
- 4
839 has no twin: neither 837 nor 841 is prime.
Primes around the 146th
| Position | Prime | Gap from the previous |
|---|---|---|
| 143 | 823 | 2 |
| 144 | 827 | 4 |
| 145 | 829 | 2 |
| 146 | 839 | 10 |
| 147 | 853 | 14 |
| 148 | 857 | 4 |
| 149 | 859 | 2 |
Questions
What is the 146th prime number?
839.
Which prime number is 839?
839 is the 146th prime number.
What is the sum of the first 146 primes?
55,837.