What is the 553rd prime number?
The 553rd prime number is 4007. The next prime is 4013 (a gap of 6) and the one before is 4003.
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 553rd one is 4007.
- 2
4007 is prime because no prime up to ā4007 ā 63.30 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 553rd prime is close to 553 Ć ln(553) ā 3492, and here it is 4007.
- 4
4007 has no twin: neither 4005 nor 4009 is prime.
Primes around the 553rd
| Position | Prime | Gap from the previous |
|---|---|---|
| 550 | 3989 | 22 |
| 551 | 4001 | 12 |
| 552 | 4003 | 2 |
| 553 | 4007 | 4 |
| 554 | 4013 | 6 |
| 555 | 4019 | 6 |
| 556 | 4021 | 2 |
Questions
What is the 553rd prime number?
4007.
Which prime number is 4007?
4007 is the 553rd prime number.
What is the sum of the first 553 primes?
1,025,518.