Prime numbers between 55001 and 56,000
There are 93 prime numbers between 55001 and 56,000: 55001, 55009, 55021, 55049, 55051, 55057, 55061, 55073, 55079, 55103, 55109, 55117, 55127, 55147, 55163, 55171, 55201, 55207, 55213, 55217, 55219, 55229, 55243, 55249, 55259, 55291, 55313, 55331, 55333, 55337, 55339, 55343, 55351, 55373, 55381, 55399, 55411, 55439, 55441, 55457, 55469, 55487, 55501, 55511, 55529, 55541, 55547, 55579, 55589, 55603, 55609, 55619, 55621, 55631, 55633, 55639, 55661, 55663, 55667, 55673, 55681, 55691, 55697, 55711, 55717, 55721, 55733, 55763, 55787, 55793, 55799, 55807, 55813, 55817, 55819, 55823, 55829, 55837, 55843, 55849, 55871, 55889, 55897, 55901, 55903, 55921, 55927, 55931, 55933, 55949, 55967, 55987, 55997.
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 ā56000 ā 236.6 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 93 primes between 55001 and 56,000, with a total of 5,163,289.
- 3
The biggest gap between neighbouring primes in this range is 32, after 55259 (the next prime is 55291). There are 11 twin prime pairs (primes 2 apart): (55049, 55051), (55217, 55219), (55331, 55333), (55337, 55339), (55439, 55441), (55619, 55621), (55631, 55633), (55661, 55663), (55817, 55819), (55901, 55903), (55931, 55933).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 55,001 to 56,000 | 93 | 9.3% |
Questions
How many prime numbers are there between 55001 and 56,000?
93.
What is the biggest prime number below 56,000?
55997.
What is the first prime number after 55000?
55001.