What is the 503rd prime number?
The 503rd prime number is 3593. The next prime is 3607 (a gap of 14) and the one before is 3583.
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 503rd one is 3593.
- 2
3593 is prime because no prime up to ā3593 ā 59.94 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 503rd prime is close to 503 Ć ln(503) ā 3129, and here it is 3593.
- 4
3593 has no twin: neither 3591 nor 3595 is prime.
Primes around the 503rd
| Position | Prime | Gap from the previous |
|---|---|---|
| 500 | 3571 | 12 |
| 501 | 3581 | 10 |
| 502 | 3583 | 2 |
| 503 | 3593 | 10 |
| 504 | 3607 | 14 |
| 505 | 3613 | 6 |
| 506 | 3617 | 4 |
Questions
What is the 503rd prime number?
3593.
Which prime number is 3593?
3593 is the 503rd prime number.
What is the sum of the first 503 primes?
835,450.