What is the 5100th prime number?
The 5100th prime number is 49663. The next prime is 49667 (a gap of 4) and the one before is 49639.
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 5100th one is 49663.
- 2
49663 is prime because no prime up to ā49663 ā 222.85 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 5100th prime is close to 5100 Ć ln(5100) ā 43539, and here it is 49663.
- 4
49663 has no twin: neither 49661 nor 49665 is prime.
Primes around the 5100th
| Position | Prime | Gap from the previous |
|---|---|---|
| 5097 | 49627 | 14 |
| 5098 | 49633 | 6 |
| 5099 | 49639 | 6 |
| 5100 | 49663 | 24 |
| 5101 | 49667 | 4 |
| 5102 | 49669 | 2 |
| 5103 | 49681 | 12 |
Questions
What is the 5100th prime number?
49663.
Which prime number is 49663?
49663 is the 5100th prime number.
What is the sum of the first 5100 primes?
119,368,879.