Prime numbers between 59001 and 60,000
There are 94 prime numbers between 59001 and 60,000: 59009, 59011, 59021, 59023, 59029, 59051, 59053, 59063, 59069, 59077, 59083, 59093, 59107, 59113, 59119, 59123, 59141, 59149, 59159, 59167, 59183, 59197, 59207, 59209, 59219, 59221, 59233, 59239, 59243, 59263, 59273, 59281, 59333, 59341, 59351, 59357, 59359, 59369, 59377, 59387, 59393, 59399, 59407, 59417, 59419, 59441, 59443, 59447, 59453, 59467, 59471, 59473, 59497, 59509, 59513, 59539, 59557, 59561, 59567, 59581, 59611, 59617, 59621, 59627, 59629, 59651, 59659, 59663, 59669, 59671, 59693, 59699, 59707, 59723, 59729, 59743, 59747, 59753, 59771, 59779, 59791, 59797, 59809, 59833, 59863, 59879, 59887, 59921, 59929, 59951, 59957, 59971, 59981, 59999.
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 ā60000 ā 244.9 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 94 primes between 59001 and 60,000, with a total of 5,589,186.
- 3
The biggest gap between neighbouring primes in this range is 52, after 59281 (the next prime is 59333). There are 11 twin prime pairs (primes 2 apart): (59009, 59011), (59021, 59023), (59051, 59053), (59207, 59209), (59219, 59221), (59357, 59359), (59417, 59419), (59441, 59443), (59471, 59473), (59627, 59629), (59669, 59671).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 59,001 to 60,000 | 94 | 9.4% |
Questions
How many prime numbers are there between 59001 and 60,000?
94.
What is the biggest prime number below 60,000?
59999.
What is the first prime number after 59000?
59009.