What is the 4003rd prime number?
The 4003rd prime number is 37853. The next prime is 37861 (a gap of 8) and the one before is 37847.
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 4003rd one is 37853.
- 2
37853 is prime because no prime up to ā37853 ā 194.56 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 4003rd prime is close to 4003 Ć ln(4003) ā 33204, and here it is 37853.
- 4
37853 has no twin: neither 37851 nor 37855 is prime.
Primes around the 4003rd
| Position | Prime | Gap from the previous |
|---|---|---|
| 4000 | 37813 | 2 |
| 4001 | 37831 | 18 |
| 4002 | 37847 | 16 |
| 4003 | 37853 | 6 |
| 4004 | 37861 | 8 |
| 4005 | 37871 | 10 |
| 4006 | 37879 | 8 |
Questions
What is the 4003rd prime number?
37853.
Which prime number is 37853?
37853 is the 4003rd prime number.
What is the sum of the first 4003 primes?
71,380,438.