What is the 4004th prime number?
The 4004th prime number is 37861. The next prime is 37871 (a gap of 10) and the one before is 37853.
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 4004th one is 37861.
- 2
37861 is prime because no prime up to ā37861 ā 194.58 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 4004th prime is close to 4004 Ć ln(4004) ā 33213, and here it is 37861.
- 4
37861 has no twin: neither 37859 nor 37863 is prime.
Primes around the 4004th
| Position | Prime | Gap from the previous |
|---|---|---|
| 4001 | 37831 | 18 |
| 4002 | 37847 | 16 |
| 4003 | 37853 | 6 |
| 4004 | 37861 | 8 |
| 4005 | 37871 | 10 |
| 4006 | 37879 | 8 |
| 4007 | 37889 | 10 |
Questions
What is the 4004th prime number?
37861.
Which prime number is 37861?
37861 is the 4004th prime number.
What is the sum of the first 4004 primes?
71,418,299.