What is the 5040th prime number?
The 5040th prime number is 49033. The next prime is 49037 (a gap of 4) and the one before is 49031.
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 5040th one is 49033.
- 2
49033 is prime because no prime up to ā49033 ā 221.43 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 5040th prime is close to 5040 Ć ln(5040) ā 42967, and here it is 49033.
- 4
49033 is a twin prime: 49031 and 49033 are both prime.
Primes around the 5040th
| Position | Prime | Gap from the previous |
|---|---|---|
| 5037 | 49009 | 6 |
| 5038 | 49019 | 10 |
| 5039 | 49031 | 12 |
| 5040 | 49033 | 2 |
| 5041 | 49037 | 4 |
| 5042 | 49043 | 6 |
| 5043 | 49057 | 14 |
Questions
What is the 5040th prime number?
49033.
Which prime number is 49033?
49033 is the 5040th prime number.
What is the sum of the first 5040 primes?
116,408,333.