What is the 1653rd prime number?
The 1653rd prime number is 14009. The next prime is 14011 (a gap of 2) and the one before is 13999.
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 1653rd one is 14009.
- 2
14009 is prime because no prime up to ā14009 ā 118.36 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 1653rd prime is close to 1653 Ć ln(1653) ā 12249, and here it is 14009.
- 4
14009 is a twin prime: 14009 and 14011 are both prime.
Primes around the 1653rd
| Position | Prime | Gap from the previous |
|---|---|---|
| 1650 | 13967 | 4 |
| 1651 | 13997 | 30 |
| 1652 | 13999 | 2 |
| 1653 | 14009 | 10 |
| 1654 | 14011 | 2 |
| 1655 | 14029 | 18 |
| 1656 | 14033 | 4 |
Questions
What is the 1653rd prime number?
14009.
Which prime number is 14009?
14009 is the 1653rd prime number.
What is the sum of the first 1653 primes?
10,828,600.