Prime numbers between 46001 and 47,000
There are 90 prime numbers between 46001 and 47,000: 46021, 46027, 46049, 46051, 46061, 46073, 46091, 46093, 46099, 46103, 46133, 46141, 46147, 46153, 46171, 46181, 46183, 46187, 46199, 46219, 46229, 46237, 46261, 46271, 46273, 46279, 46301, 46307, 46309, 46327, 46337, 46349, 46351, 46381, 46399, 46411, 46439, 46441, 46447, 46451, 46457, 46471, 46477, 46489, 46499, 46507, 46511, 46523, 46549, 46559, 46567, 46573, 46589, 46591, 46601, 46619, 46633, 46639, 46643, 46649, 46663, 46679, 46681, 46687, 46691, 46703, 46723, 46727, 46747, 46751, 46757, 46769, 46771, 46807, 46811, 46817, 46819, 46829, 46831, 46853, 46861, 46867, 46877, 46889, 46901, 46919, 46933, 46957, 46993, 46997.
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 ā47000 ā 216.8 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 90 primes between 46001 and 47,000, with a total of 4,184,638.
- 3
The biggest gap between neighbouring primes in this range is 36, after 46771 (the next prime is 46807). There are 12 twin prime pairs (primes 2 apart): (46049, 46051), (46091, 46093), (46181, 46183), (46271, 46273), (46307, 46309), (46349, 46351), (46439, 46441), (46589, 46591), (46679, 46681), (46769, 46771), (46817, 46819), (46829, 46831).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 46,001 to 47,000 | 90 | 9% |
Questions
How many prime numbers are there between 46001 and 47,000?
90.
What is the biggest prime number below 47,000?
46997.
What is the first prime number after 46000?
46021.