What is the 137th prime number?
The 137th prime number is 773. The next prime is 787 (a gap of 14) and the one before is 769.
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 137th one is 773.
- 2
773 is prime because no prime up to ā773 ā 27.80 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 137th prime is close to 137 Ć ln(137) ā 674, and here it is 773.
- 4
773 has no twin: neither 771 nor 775 is prime.
Primes around the 137th
| Position | Prime | Gap from the previous |
|---|---|---|
| 134 | 757 | 6 |
| 135 | 761 | 4 |
| 136 | 769 | 8 |
| 137 | 773 | 4 |
| 138 | 787 | 14 |
| 139 | 797 | 10 |
| 140 | 809 | 12 |
Questions
What is the 137th prime number?
773.
Which prime number is 773?
773 is the 137th prime number.
What is the sum of the first 137 primes?
48,494.