What is the 97th prime number?
The 97th prime number is 509. The next prime is 521 (a gap of 12) and the one before is 503.
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 97th one is 509.
- 2
509 is prime because no prime up to ā509 ā 22.56 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 97th prime is close to 97 Ć ln(97) ā 444, and here it is 509.
- 4
509 has no twin: neither 507 nor 511 is prime.
Primes around the 97th
| Position | Prime | Gap from the previous |
|---|---|---|
| 94 | 491 | 4 |
| 95 | 499 | 8 |
| 96 | 503 | 4 |
| 97 | 509 | 6 |
| 98 | 521 | 12 |
| 99 | 523 | 2 |
| 100 | 541 | 18 |
Questions
What is the 97th prime number?
509.
Which prime number is 509?
509 is the 97th prime number.
What is the sum of the first 97 primes?
22,548.