What is the 4205th prime number?
The 4205th prime number is 40013. The next prime is 40031 (a gap of 18) and the one before is 40009.
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 4205th one is 40013.
- 2
40013 is prime because no prime up to ā40013 ā 200.03 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 4205th prime is close to 4205 Ć ln(4205) ā 35087, and here it is 40013.
- 4
40013 has no twin: neither 40011 nor 40015 is prime.
Primes around the 4205th
| Position | Prime | Gap from the previous |
|---|---|---|
| 4202 | 39983 | 4 |
| 4203 | 39989 | 6 |
| 4204 | 40009 | 20 |
| 4205 | 40013 | 4 |
| 4206 | 40031 | 18 |
| 4207 | 40037 | 6 |
| 4208 | 40039 | 2 |
Questions
What is the 4205th prime number?
40013.
Which prime number is 40013?
40013 is the 4205th prime number.
What is the sum of the first 4205 primes?
79,250,688.