Prime numbers between 47001 and 48,000
There are 95 prime numbers between 47001 and 48,000: 47017, 47041, 47051, 47057, 47059, 47087, 47093, 47111, 47119, 47123, 47129, 47137, 47143, 47147, 47149, 47161, 47189, 47207, 47221, 47237, 47251, 47269, 47279, 47287, 47293, 47297, 47303, 47309, 47317, 47339, 47351, 47353, 47363, 47381, 47387, 47389, 47407, 47417, 47419, 47431, 47441, 47459, 47491, 47497, 47501, 47507, 47513, 47521, 47527, 47533, 47543, 47563, 47569, 47581, 47591, 47599, 47609, 47623, 47629, 47639, 47653, 47657, 47659, 47681, 47699, 47701, 47711, 47713, 47717, 47737, 47741, 47743, 47777, 47779, 47791, 47797, 47807, 47809, 47819, 47837, 47843, 47857, 47869, 47881, 47903, 47911, 47917, 47933, 47939, 47947, 47951, 47963, 47969, 47977, 47981.
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 ā48000 ā 219.1 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 95 primes between 47001 and 48,000, with a total of 4,513,925.
- 3
The biggest gap between neighbouring primes in this range is 34, after 47743 (the next prime is 47777). There are 11 twin prime pairs (primes 2 apart): (47057, 47059), (47147, 47149), (47351, 47353), (47387, 47389), (47417, 47419), (47657, 47659), (47699, 47701), (47711, 47713), (47741, 47743), (47777, 47779), (47807, 47809).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 47,001 to 48,000 | 95 | 9.5% |
Questions
How many prime numbers are there between 47001 and 48,000?
95.
What is the biggest prime number below 48,000?
47981.
What is the first prime number after 47000?
47017.