Prime numbers between 54001 and 55,000
There are 90 prime numbers between 54001 and 55,000: 54001, 54011, 54013, 54037, 54049, 54059, 54083, 54091, 54101, 54121, 54133, 54139, 54151, 54163, 54167, 54181, 54193, 54217, 54251, 54269, 54277, 54287, 54293, 54311, 54319, 54323, 54331, 54347, 54361, 54367, 54371, 54377, 54401, 54403, 54409, 54413, 54419, 54421, 54437, 54443, 54449, 54469, 54493, 54497, 54499, 54503, 54517, 54521, 54539, 54541, 54547, 54559, 54563, 54577, 54581, 54583, 54601, 54617, 54623, 54629, 54631, 54647, 54667, 54673, 54679, 54709, 54713, 54721, 54727, 54751, 54767, 54773, 54779, 54787, 54799, 54829, 54833, 54851, 54869, 54877, 54881, 54907, 54917, 54919, 54941, 54949, 54959, 54973, 54979, 54983.
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 ā55000 ā 234.5 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 90 primes between 54001 and 55,000, with a total of 4,905,138.
- 3
The biggest gap between neighbouring primes in this range is 34, after 54217 (the next prime is 54251). There are 8 twin prime pairs (primes 2 apart): (54011, 54013), (54401, 54403), (54419, 54421), (54497, 54499), (54539, 54541), (54581, 54583), (54629, 54631), (54917, 54919).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 54,001 to 55,000 | 90 | 9% |
Questions
How many prime numbers are there between 54001 and 55,000?
90.
What is the biggest prime number below 55,000?
54983.
What is the first prime number after 54000?
54001.