What is the 3972nd prime number?
The 3972nd prime number is 37517. The next prime is 37529 (a gap of 12) and the one before is 37511.
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 3972nd one is 37517.
- 2
37517 is prime because no prime up to ā37517 ā 193.69 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3972nd prime is close to 3972 Ć ln(3972) ā 32916, and here it is 37517.
- 4
37517 has no twin: neither 37515 nor 37519 is prime.
Primes around the 3972nd
| Position | Prime | Gap from the previous |
|---|---|---|
| 3969 | 37501 | 8 |
| 3970 | 37507 | 6 |
| 3971 | 37511 | 4 |
| 3972 | 37517 | 6 |
| 3973 | 37529 | 12 |
| 3974 | 37537 | 8 |
| 3975 | 37547 | 10 |
Questions
What is the 3972nd prime number?
37517.
Which prime number is 37517?
37517 is the 3972nd prime number.
What is the sum of the first 3972 primes?
70,212,709.