Prime numbers between 62001 and 63,000
There are 88 prime numbers between 62001 and 63,000: 62003, 62011, 62017, 62039, 62047, 62053, 62057, 62071, 62081, 62099, 62119, 62129, 62131, 62137, 62141, 62143, 62171, 62189, 62191, 62201, 62207, 62213, 62219, 62233, 62273, 62297, 62299, 62303, 62311, 62323, 62327, 62347, 62351, 62383, 62401, 62417, 62423, 62459, 62467, 62473, 62477, 62483, 62497, 62501, 62507, 62533, 62539, 62549, 62563, 62581, 62591, 62597, 62603, 62617, 62627, 62633, 62639, 62653, 62659, 62683, 62687, 62701, 62723, 62731, 62743, 62753, 62761, 62773, 62791, 62801, 62819, 62827, 62851, 62861, 62869, 62873, 62897, 62903, 62921, 62927, 62929, 62939, 62969, 62971, 62981, 62983, 62987, 62989.
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 ā63000 ā 251.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 88 primes between 62001 and 63,000, with a total of 5,500,248.
- 3
The biggest gap between neighbouring primes in this range is 40, after 62233 (the next prime is 62273). There are 8 twin prime pairs (primes 2 apart): (62129, 62131), (62141, 62143), (62189, 62191), (62297, 62299), (62927, 62929), (62969, 62971), (62981, 62983), (62987, 62989).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 62,001 to 63,000 | 88 | 8.8% |
Questions
How many prime numbers are there between 62001 and 63,000?
88.
What is the biggest prime number below 63,000?
62989.
What is the first prime number after 62000?
62003.