What is the 4045th prime number?
The 4045th prime number is 38321. The next prime is 38327 (a gap of 6) and the one before is 38317.
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 4045th one is 38321.
- 2
38321 is prime because no prime up to ā38321 ā 195.76 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 4045th prime is close to 4045 Ć ln(4045) ā 33595, and here it is 38321.
- 4
38321 has no twin: neither 38319 nor 38323 is prime.
Primes around the 4045th
| Position | Prime | Gap from the previous |
|---|---|---|
| 4042 | 38299 | 12 |
| 4043 | 38303 | 4 |
| 4044 | 38317 | 14 |
| 4045 | 38321 | 4 |
| 4046 | 38327 | 6 |
| 4047 | 38329 | 2 |
| 4048 | 38333 | 4 |
Questions
What is the 4045th prime number?
38321.
Which prime number is 38321?
38321 is the 4045th prime number.
What is the sum of the first 4045 primes?
72,980,766.