What is the 5101st prime number?
The 5101st prime number is 49667. The next prime is 49669 (a gap of 2) and the one before is 49663.
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 5101st one is 49667.
- 2
49667 is prime because no prime up to ā49667 ā 222.86 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 5101st prime is close to 5101 Ć ln(5101) ā 43548, and here it is 49667.
- 4
49667 is a twin prime: 49667 and 49669 are both prime.
Primes around the 5101st
| Position | Prime | Gap from the previous |
|---|---|---|
| 5098 | 49633 | 6 |
| 5099 | 49639 | 6 |
| 5100 | 49663 | 24 |
| 5101 | 49667 | 4 |
| 5102 | 49669 | 2 |
| 5103 | 49681 | 12 |
| 5104 | 49697 | 16 |
Questions
What is the 5101st prime number?
49667.
Which prime number is 49667?
49667 is the 5101st prime number.
What is the sum of the first 5101 primes?
119,418,546.