What is the 150th prime number?
The 150th prime number is 863. The next prime is 877 (a gap of 14) and the one before is 859.
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 150th one is 863.
- 2
863 is prime because no prime up to ā863 ā 29.38 divides it.
- 3
The primes are spread thinner as numbers grow: by the prime number theorem the 150th prime is close to 150 Ć ln(150) ā 752, and here it is 863.
- 4
863 has no twin: neither 861 nor 865 is prime.
Primes around the 150th
| Position | Prime | Gap from the previous |
|---|---|---|
| 147 | 853 | 14 |
| 148 | 857 | 4 |
| 149 | 859 | 2 |
| 150 | 863 | 4 |
| 151 | 877 | 14 |
| 152 | 881 | 4 |
| 153 | 883 | 2 |
Questions
What is the 150th prime number?
863.
Which prime number is 863?
863 is the 150th prime number.
What is the sum of the first 150 primes?
59,269.