What is the 4013th prime number?
The 4013th prime number is 37967. The next prime is 37987 (a gap of 20) and the one before is 37963.
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 4013th one is 37967.
- 2
37967 is prime because no prime up to ā37967 ā 194.85 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 4013th prime is close to 4013 Ć ln(4013) ā 33297, and here it is 37967.
- 4
37967 has no twin: neither 37965 nor 37969 is prime.
Primes around the 4013th
| Position | Prime | Gap from the previous |
|---|---|---|
| 4010 | 37951 | 44 |
| 4011 | 37957 | 6 |
| 4012 | 37963 | 6 |
| 4013 | 37967 | 4 |
| 4014 | 37987 | 20 |
| 4015 | 37991 | 4 |
| 4016 | 37993 | 2 |
Questions
What is the 4013th prime number?
37967.
Which prime number is 37967?
37967 is the 4013th prime number.
What is the sum of the first 4013 primes?
71,759,580.