What is the 965th prime number?
The 965th prime number is 7591. The next prime is 7603 (a gap of 12) and the one before is 7589.
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 965th one is 7591.
- 2
7591 is prime because no prime up to ā7591 ā 87.13 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 965th prime is close to 965 Ć ln(965) ā 6632, and here it is 7591.
- 4
7591 is a twin prime: 7589 and 7591 are both prime.
Primes around the 965th
| Position | Prime | Gap from the previous |
|---|---|---|
| 962 | 7577 | 4 |
| 963 | 7583 | 6 |
| 964 | 7589 | 6 |
| 965 | 7591 | 2 |
| 966 | 7603 | 12 |
| 967 | 7607 | 4 |
| 968 | 7621 | 14 |
Questions
What is the 965th prime number?
7591.
Which prime number is 7591?
7591 is the 965th prime number.
What is the sum of the first 965 primes?
3,411,320.