What is the 138th prime number?
The 138th prime number is 787. The next prime is 797 (a gap of 10) and the one before is 773.
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 138th one is 787.
- 2
787 is prime because no prime up to ā787 ā 28.05 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 138th prime is close to 138 Ć ln(138) ā 680, and here it is 787.
- 4
787 has no twin: neither 785 nor 789 is prime.
Primes around the 138th
| Position | Prime | Gap from the previous |
|---|---|---|
| 135 | 761 | 4 |
| 136 | 769 | 8 |
| 137 | 773 | 4 |
| 138 | 787 | 14 |
| 139 | 797 | 10 |
| 140 | 809 | 12 |
| 141 | 811 | 2 |
Questions
What is the 138th prime number?
787.
Which prime number is 787?
787 is the 138th prime number.
What is the sum of the first 138 primes?
49,281.