What is the 1238th prime number?
The 1238th prime number is 10091. The next prime is 10093 (a gap of 2) and the one before is 10079.
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 1238th one is 10091.
- 2
10091 is prime because no prime up to ā10091 ā 100.45 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 1238th prime is close to 1238 Ć ln(1238) ā 8816, and here it is 10091.
- 4
10091 is a twin prime: 10091 and 10093 are both prime.
Primes around the 1238th
| Position | Prime | Gap from the previous |
|---|---|---|
| 1235 | 10067 | 6 |
| 1236 | 10069 | 2 |
| 1237 | 10079 | 10 |
| 1238 | 10091 | 12 |
| 1239 | 10093 | 2 |
| 1240 | 10099 | 6 |
| 1241 | 10103 | 4 |
Questions
What is the 1238th prime number?
10091.
Which prime number is 10091?
10091 is the 1238th prime number.
What is the sum of the first 1238 primes?
5,826,855.