Prime numbers between 31001 and 32,000
There are 92 prime numbers between 31001 and 32,000: 31013, 31019, 31033, 31039, 31051, 31063, 31069, 31079, 31081, 31091, 31121, 31123, 31139, 31147, 31151, 31153, 31159, 31177, 31181, 31183, 31189, 31193, 31219, 31223, 31231, 31237, 31247, 31249, 31253, 31259, 31267, 31271, 31277, 31307, 31319, 31321, 31327, 31333, 31337, 31357, 31379, 31387, 31391, 31393, 31397, 31469, 31477, 31481, 31489, 31511, 31513, 31517, 31531, 31541, 31543, 31547, 31567, 31573, 31583, 31601, 31607, 31627, 31643, 31649, 31657, 31663, 31667, 31687, 31699, 31721, 31723, 31727, 31729, 31741, 31751, 31769, 31771, 31793, 31799, 31817, 31847, 31849, 31859, 31873, 31883, 31891, 31907, 31957, 31963, 31973, 31981, 31991.
How to work it out
- 1
A prime has exactly two factors, 1 and itself. To list them, cross out multiples of 2, then 3, then 5, and so on up to ā32000 ā 178.9 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 92 primes between 31001 and 32,000, with a total of 2,894,592.
- 3
The biggest gap between neighbouring primes in this range is 72, after 31397 (the next prime is 31469). There are 13 twin prime pairs (primes 2 apart), the first ones (31079, 31081), (31121, 31123), (31151, 31153), (31181, 31183), (31247, 31249), (31319, 31321), (31391, 31393), (31511, 31513).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 31,001 to 32,000 | 92 | 9.2% |
Questions
How many prime numbers are there between 31001 and 32,000?
92.
What is the biggest prime number below 32,000?
31991.
What is the first prime number after 31000?
31013.