What is the 296th prime number?
The 296th prime number is 1949. The next prime is 1951 (a gap of 2) and the one before is 1933.
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 296th one is 1949.
- 2
1949 is prime because no prime up to ā1949 ā 44.15 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 296th prime is close to 296 Ć ln(296) ā 1684, and here it is 1949.
- 4
1949 is a twin prime: 1949 and 1951 are both prime.
Primes around the 296th
| Position | Prime | Gap from the previous |
|---|---|---|
| 293 | 1913 | 6 |
| 294 | 1931 | 18 |
| 295 | 1933 | 2 |
| 296 | 1949 | 16 |
| 297 | 1951 | 2 |
| 298 | 1973 | 22 |
| 299 | 1979 | 6 |
Questions
What is the 296th prime number?
1949.
Which prime number is 1949?
1949 is the 296th prime number.
What is the sum of the first 296 primes?
263,171.