What is the 100th prime number?
The 100th prime number is 541. The next prime is 547 (a gap of 6) and the one before is 523.
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 100th one is 541.
- 2
541 is prime because no prime up to ā541 ā 23.26 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 100th prime is close to 100 Ć ln(100) ā 461, and here it is 541.
- 4
541 has no twin: neither 539 nor 543 is prime.
Primes around the 100th
| Position | Prime | Gap from the previous |
|---|---|---|
| 97 | 509 | 6 |
| 98 | 521 | 12 |
| 99 | 523 | 2 |
| 100 | 541 | 18 |
| 101 | 547 | 6 |
| 102 | 557 | 10 |
| 103 | 563 | 6 |
Questions
What is the 100th prime number?
541.
Which prime number is 541?
541 is the 100th prime number.
What is the sum of the first 100 primes?
24,133.