Prime numbers between 45001 and 46,000
There are 86 prime numbers between 45001 and 46,000: 45007, 45013, 45053, 45061, 45077, 45083, 45119, 45121, 45127, 45131, 45137, 45139, 45161, 45179, 45181, 45191, 45197, 45233, 45247, 45259, 45263, 45281, 45289, 45293, 45307, 45317, 45319, 45329, 45337, 45341, 45343, 45361, 45377, 45389, 45403, 45413, 45427, 45433, 45439, 45481, 45491, 45497, 45503, 45523, 45533, 45541, 45553, 45557, 45569, 45587, 45589, 45599, 45613, 45631, 45641, 45659, 45667, 45673, 45677, 45691, 45697, 45707, 45737, 45751, 45757, 45763, 45767, 45779, 45817, 45821, 45823, 45827, 45833, 45841, 45853, 45863, 45869, 45887, 45893, 45943, 45949, 45953, 45959, 45971, 45979, 45989.
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 ā46000 ā 214.5 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 86 primes between 45001 and 46,000, with a total of 3,913,680.
- 3
The biggest gap between neighbouring primes in this range is 50, after 45893 (the next prime is 45943). There are 7 twin prime pairs (primes 2 apart): (45119, 45121), (45137, 45139), (45179, 45181), (45317, 45319), (45341, 45343), (45587, 45589), (45821, 45823).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 45,001 to 46,000 | 86 | 8.6% |
Questions
How many prime numbers are there between 45001 and 46,000?
86.
What is the biggest prime number below 46,000?
45989.
What is the first prime number after 45000?
45007.