What is the 101st prime number?
The 101st prime number is 547. The next prime is 557 (a gap of 10) and the one before is 541.
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 101st one is 547.
- 2
547 is prime because no prime up to ā547 ā 23.39 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 101st prime is close to 101 Ć ln(101) ā 466, and here it is 547.
- 4
547 has no twin: neither 545 nor 549 is prime.
Primes around the 101st
| Position | Prime | Gap from the previous |
|---|---|---|
| 98 | 521 | 12 |
| 99 | 523 | 2 |
| 100 | 541 | 18 |
| 101 | 547 | 6 |
| 102 | 557 | 10 |
| 103 | 563 | 6 |
| 104 | 569 | 6 |
Questions
What is the 101st prime number?
547.
Which prime number is 547?
547 is the 101st prime number.
What is the sum of the first 101 primes?
24,680.