Prime numbers between 63001 and 64,000
There are 93 prime numbers between 63001 and 64,000: 63029, 63031, 63059, 63067, 63073, 63079, 63097, 63103, 63113, 63127, 63131, 63149, 63179, 63197, 63199, 63211, 63241, 63247, 63277, 63281, 63299, 63311, 63313, 63317, 63331, 63337, 63347, 63353, 63361, 63367, 63377, 63389, 63391, 63397, 63409, 63419, 63421, 63439, 63443, 63463, 63467, 63473, 63487, 63493, 63499, 63521, 63527, 63533, 63541, 63559, 63577, 63587, 63589, 63599, 63601, 63607, 63611, 63617, 63629, 63647, 63649, 63659, 63667, 63671, 63689, 63691, 63697, 63703, 63709, 63719, 63727, 63737, 63743, 63761, 63773, 63781, 63793, 63799, 63803, 63809, 63823, 63839, 63841, 63853, 63857, 63863, 63901, 63907, 63913, 63929, 63949, 63977, 63997.
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 ā64000 ā 253.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 93 primes between 63001 and 64,000, with a total of 5,906,767.
- 3
The biggest gap between neighbouring primes in this range is 38, after 63863 (the next prime is 63901). There are 10 twin prime pairs (primes 2 apart): (63029, 63031), (63197, 63199), (63311, 63313), (63389, 63391), (63419, 63421), (63587, 63589), (63599, 63601), (63647, 63649), (63689, 63691), (63839, 63841).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 63,001 to 64,000 | 93 | 9.3% |
Questions
How many prime numbers are there between 63001 and 64,000?
93.
What is the biggest prime number below 64,000?
63997.
What is the first prime number after 63000?
63029.