What is the 3978th prime number?
The 3978th prime number is 37567. The next prime is 37571 (a gap of 4) and the one before is 37561.
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 3978th one is 37567.
- 2
37567 is prime because no prime up to ā37567 ā 193.82 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 3978th prime is close to 3978 Ć ln(3978) ā 32972, and here it is 37567.
- 4
37567 has no twin: neither 37565 nor 37569 is prime.
Primes around the 3978th
| Position | Prime | Gap from the previous |
|---|---|---|
| 3975 | 37547 | 10 |
| 3976 | 37549 | 2 |
| 3977 | 37561 | 12 |
| 3978 | 37567 | 6 |
| 3979 | 37571 | 4 |
| 3980 | 37573 | 2 |
| 3981 | 37579 | 6 |
Questions
What is the 3978th prime number?
37567.
Which prime number is 37567?
37567 is the 3978th prime number.
What is the sum of the first 3978 primes?
70,437,999.