What is the 135th prime number?
The 135th prime number is 761. The next prime is 769 (a gap of 8) and the one before is 757.
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 135th one is 761.
- 2
761 is prime because no prime up to ā761 ā 27.59 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 135th prime is close to 135 Ć ln(135) ā 662, and here it is 761.
- 4
761 has no twin: neither 759 nor 763 is prime.
Primes around the 135th
| Position | Prime | Gap from the previous |
|---|---|---|
| 132 | 743 | 4 |
| 133 | 751 | 8 |
| 134 | 757 | 6 |
| 135 | 761 | 4 |
| 136 | 769 | 8 |
| 137 | 773 | 4 |
| 138 | 787 | 14 |
Questions
What is the 135th prime number?
761.
Which prime number is 761?
761 is the 135th prime number.
What is the sum of the first 135 primes?
46,952.