What is the 971st prime number?
The 971st prime number is 7649. The next prime is 7669 (a gap of 20) and the one before is 7643.
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 971st one is 7649.
- 2
7649 is prime because no prime up to ā7649 ā 87.46 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 971st prime is close to 971 Ć ln(971) ā 6679, and here it is 7649.
- 4
7649 has no twin: neither 7647 nor 7651 is prime.
Primes around the 971st
| Position | Prime | Gap from the previous |
|---|---|---|
| 968 | 7621 | 14 |
| 969 | 7639 | 18 |
| 970 | 7643 | 4 |
| 971 | 7649 | 6 |
| 972 | 7669 | 20 |
| 973 | 7673 | 4 |
| 974 | 7681 | 8 |
Questions
What is the 971st prime number?
7649.
Which prime number is 7649?
7649 is the 971st prime number.
What is the sum of the first 971 primes?
3,457,082.