Prime numbers between 52001 and 53,000
There are 89 prime numbers between 52001 and 53,000: 52009, 52021, 52027, 52051, 52057, 52067, 52069, 52081, 52103, 52121, 52127, 52147, 52153, 52163, 52177, 52181, 52183, 52189, 52201, 52223, 52237, 52249, 52253, 52259, 52267, 52289, 52291, 52301, 52313, 52321, 52361, 52363, 52369, 52379, 52387, 52391, 52433, 52453, 52457, 52489, 52501, 52511, 52517, 52529, 52541, 52543, 52553, 52561, 52567, 52571, 52579, 52583, 52609, 52627, 52631, 52639, 52667, 52673, 52691, 52697, 52709, 52711, 52721, 52727, 52733, 52747, 52757, 52769, 52783, 52807, 52813, 52817, 52837, 52859, 52861, 52879, 52883, 52889, 52901, 52903, 52919, 52937, 52951, 52957, 52963, 52967, 52973, 52981, 52999.
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 ā53000 ā 230.2 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 89 primes between 52001 and 53,000, with a total of 4,673,755.
- 3
The biggest gap between neighbouring primes in this range is 42, after 52391 (the next prime is 52433). There are 8 twin prime pairs (primes 2 apart): (52067, 52069), (52181, 52183), (52289, 52291), (52361, 52363), (52541, 52543), (52709, 52711), (52859, 52861), (52901, 52903).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 52,001 to 53,000 | 89 | 8.9% |
Questions
How many prime numbers are there between 52001 and 53,000?
89.
What is the biggest prime number below 53,000?
52999.
What is the first prime number after 52000?
52009.