What is the 148th prime number?
The 148th prime number is 857. The next prime is 859 (a gap of 2) and the one before is 853.
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 148th one is 857.
- 2
857 is prime because no prime up to ā857 ā 29.27 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 148th prime is close to 148 Ć ln(148) ā 740, and here it is 857.
- 4
857 is a twin prime: 857 and 859 are both prime.
Primes around the 148th
| Position | Prime | Gap from the previous |
|---|---|---|
| 145 | 829 | 2 |
| 146 | 839 | 10 |
| 147 | 853 | 14 |
| 148 | 857 | 4 |
| 149 | 859 | 2 |
| 150 | 863 | 4 |
| 151 | 877 | 14 |
Questions
What is the 148th prime number?
857.
Which prime number is 857?
857 is the 148th prime number.
What is the sum of the first 148 primes?
57,547.