What is the 102nd prime number?
The 102nd prime number is 557. The next prime is 563 (a gap of 6) and the one before is 547.
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 102nd one is 557.
- 2
557 is prime because no prime up to ā557 ā 23.60 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 102nd prime is close to 102 Ć ln(102) ā 472, and here it is 557.
- 4
557 has no twin: neither 555 nor 559 is prime.
Primes around the 102nd
| Position | Prime | Gap from the previous |
|---|---|---|
| 99 | 523 | 2 |
| 100 | 541 | 18 |
| 101 | 547 | 6 |
| 102 | 557 | 10 |
| 103 | 563 | 6 |
| 104 | 569 | 6 |
| 105 | 571 | 2 |
Questions
What is the 102nd prime number?
557.
Which prime number is 557?
557 is the 102nd prime number.
What is the sum of the first 102 primes?
25,237.