What is the 561st prime number?
The 561st prime number is 4073. The next prime is 4079 (a gap of 6) and the one before is 4057.
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 561st one is 4073.
- 2
4073 is prime because no prime up to ā4073 ā 63.82 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 561st prime is close to 561 Ć ln(561) ā 3551, and here it is 4073.
- 4
4073 has no twin: neither 4071 nor 4075 is prime.
Primes around the 561st
| Position | Prime | Gap from the previous |
|---|---|---|
| 558 | 4049 | 22 |
| 559 | 4051 | 2 |
| 560 | 4057 | 6 |
| 561 | 4073 | 16 |
| 562 | 4079 | 6 |
| 563 | 4091 | 12 |
| 564 | 4093 | 2 |
Questions
What is the 561st prime number?
4073.
Which prime number is 4073?
4073 is the 561st prime number.
What is the sum of the first 561 primes?
1,057,828.