What is the 5138th prime number?
The 5138th prime number is 50051. The next prime is 50053 (a gap of 2) and the one before is 50047.
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 5138th one is 50051.
- 2
50051 is prime because no prime up to ā50051 ā 223.72 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 5138th prime is close to 5138 Ć ln(5138) ā 43901, and here it is 50051.
- 4
50051 is a twin prime: 50051 and 50053 are both prime.
Primes around the 5138th
| Position | Prime | Gap from the previous |
|---|---|---|
| 5135 | 50023 | 2 |
| 5136 | 50033 | 10 |
| 5137 | 50047 | 14 |
| 5138 | 50051 | 4 |
| 5139 | 50053 | 2 |
| 5140 | 50069 | 16 |
| 5141 | 50077 | 8 |
Questions
What is the 5138th prime number?
50051.
Which prime number is 50051?
50051 is the 5138th prime number.
What is the sum of the first 5138 primes?
121,263,483.