Prime numbers between 50001 and 51,000
There are 89 prime numbers between 50001 and 51,000: 50021, 50023, 50033, 50047, 50051, 50053, 50069, 50077, 50087, 50093, 50101, 50111, 50119, 50123, 50129, 50131, 50147, 50153, 50159, 50177, 50207, 50221, 50227, 50231, 50261, 50263, 50273, 50287, 50291, 50311, 50321, 50329, 50333, 50341, 50359, 50363, 50377, 50383, 50387, 50411, 50417, 50423, 50441, 50459, 50461, 50497, 50503, 50513, 50527, 50539, 50543, 50549, 50551, 50581, 50587, 50591, 50593, 50599, 50627, 50647, 50651, 50671, 50683, 50707, 50723, 50741, 50753, 50767, 50773, 50777, 50789, 50821, 50833, 50839, 50849, 50857, 50867, 50873, 50891, 50893, 50909, 50923, 50929, 50951, 50957, 50969, 50971, 50989, 50993.
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 ā51000 ā 225.8 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 89 primes between 50001 and 51,000, with a total of 4,493,077.
- 3
The biggest gap between neighbouring primes in this range is 36, after 50461 (the next prime is 50497). There are 9 twin prime pairs (primes 2 apart): (50021, 50023), (50051, 50053), (50129, 50131), (50261, 50263), (50459, 50461), (50549, 50551), (50591, 50593), (50891, 50893), (50969, 50971).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 50,001 to 51,000 | 89 | 8.9% |
Questions
How many prime numbers are there between 50001 and 51,000?
89.
What is the biggest prime number below 51,000?
50993.
What is the first prime number after 50000?
50021.