What is the 31st prime number?
The 31st prime number is 127. The next prime is 131 (a gap of 4) and the one before is 113.
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 31st one is 127.
- 2
127 is prime because no prime up to ā127 ā 11.27 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 31st prime is close to 31 Ć ln(31) ā 106, and here it is 127.
- 4
127 has no twin: neither 125 nor 129 is prime.
Primes around the 31st
| Position | Prime | Gap from the previous |
|---|---|---|
| 28 | 107 | 4 |
| 29 | 109 | 2 |
| 30 | 113 | 4 |
| 31 | 127 | 14 |
| 32 | 131 | 4 |
| 33 | 137 | 6 |
| 34 | 139 | 2 |
Questions
What is the 31st prime number?
127.
Which prime number is 127?
127 is the 31st prime number.
What is the sum of the first 31 primes?
1,720.