What is the 37th prime number?
The 37th prime number is 157. The next prime is 163 (a gap of 6) and the one before is 151.
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 37th one is 157.
- 2
157 is prime because no prime up to ā157 ā 12.53 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 37th prime is close to 37 Ć ln(37) ā 134, and here it is 157.
- 4
157 has no twin: neither 155 nor 159 is prime.
Primes around the 37th
| Position | Prime | Gap from the previous |
|---|---|---|
| 34 | 139 | 2 |
| 35 | 149 | 10 |
| 36 | 151 | 2 |
| 37 | 157 | 6 |
| 38 | 163 | 6 |
| 39 | 167 | 4 |
| 40 | 173 | 6 |
Questions
What is the 37th prime number?
157.
Which prime number is 157?
157 is the 37th prime number.
What is the sum of the first 37 primes?
2,584.