Prime numbers between 30001 and 31,000
There are 95 prime numbers between 30001 and 31,000: 30011, 30013, 30029, 30047, 30059, 30071, 30089, 30091, 30097, 30103, 30109, 30113, 30119, 30133, 30137, 30139, 30161, 30169, 30181, 30187, 30197, 30203, 30211, 30223, 30241, 30253, 30259, 30269, 30271, 30293, 30307, 30313, 30319, 30323, 30341, 30347, 30367, 30389, 30391, 30403, 30427, 30431, 30449, 30467, 30469, 30491, 30493, 30497, 30509, 30517, 30529, 30539, 30553, 30557, 30559, 30577, 30593, 30631, 30637, 30643, 30649, 30661, 30671, 30677, 30689, 30697, 30703, 30707, 30713, 30727, 30757, 30763, 30773, 30781, 30803, 30809, 30817, 30829, 30839, 30841, 30851, 30853, 30859, 30869, 30871, 30881, 30893, 30911, 30931, 30937, 30941, 30949, 30971, 30977, 30983.
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 ā31000 ā 176.1 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 95 primes between 30001 and 31,000, with a total of 2,897,129.
- 3
The biggest gap between neighbouring primes in this range is 38, after 30593 (the next prime is 30631). There are 11 twin prime pairs (primes 2 apart): (30011, 30013), (30089, 30091), (30137, 30139), (30269, 30271), (30389, 30391), (30467, 30469), (30491, 30493), (30557, 30559), (30839, 30841), (30851, 30853), (30869, 30871).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 30,001 to 31,000 | 95 | 9.5% |
Questions
How many prime numbers are there between 30001 and 31,000?
95.
What is the biggest prime number below 31,000?
30983.
What is the first prime number after 30000?
30011.