Prime numbers between 33001 and 34,000
There are 100 prime numbers between 33001 and 34,000: 33013, 33023, 33029, 33037, 33049, 33053, 33071, 33073, 33083, 33091, 33107, 33113, 33119, 33149, 33151, 33161, 33179, 33181, 33191, 33199, 33203, 33211, 33223, 33247, 33287, 33289, 33301, 33311, 33317, 33329, 33331, 33343, 33347, 33349, 33353, 33359, 33377, 33391, 33403, 33409, 33413, 33427, 33457, 33461, 33469, 33479, 33487, 33493, 33503, 33521, 33529, 33533, 33547, 33563, 33569, 33577, 33581, 33587, 33589, 33599, 33601, 33613, 33617, 33619, 33623, 33629, 33637, 33641, 33647, 33679, 33703, 33713, 33721, 33739, 33749, 33751, 33757, 33767, 33769, 33773, 33791, 33797, 33809, 33811, 33827, 33829, 33851, 33857, 33863, 33871, 33889, 33893, 33911, 33923, 33931, 33937, 33941, 33961, 33967, 33997.
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 ā34000 ā 184.4 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 100 primes between 33001 and 34,000, with a total of 3,350,240.
- 3
The biggest gap between neighbouring primes in this range is 40, after 33247 (the next prime is 33287). There are 13 twin prime pairs (primes 2 apart), the first ones (33071, 33073), (33149, 33151), (33179, 33181), (33287, 33289), (33329, 33331), (33347, 33349), (33587, 33589), (33599, 33601).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 33,001 to 34,000 | 100 | 10% |
Questions
How many prime numbers are there between 33001 and 34,000?
100.
What is the biggest prime number below 34,000?
33997.
What is the first prime number after 33000?
33013.