Prime numbers between 38001 and 39,000
There are 90 prime numbers between 38001 and 39,000: 38011, 38039, 38047, 38053, 38069, 38083, 38113, 38119, 38149, 38153, 38167, 38177, 38183, 38189, 38197, 38201, 38219, 38231, 38237, 38239, 38261, 38273, 38281, 38287, 38299, 38303, 38317, 38321, 38327, 38329, 38333, 38351, 38371, 38377, 38393, 38431, 38447, 38449, 38453, 38459, 38461, 38501, 38543, 38557, 38561, 38567, 38569, 38593, 38603, 38609, 38611, 38629, 38639, 38651, 38653, 38669, 38671, 38677, 38693, 38699, 38707, 38711, 38713, 38723, 38729, 38737, 38747, 38749, 38767, 38783, 38791, 38803, 38821, 38833, 38839, 38851, 38861, 38867, 38873, 38891, 38903, 38917, 38921, 38923, 38933, 38953, 38959, 38971, 38977, 38993.
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 ā39000 ā 197.5 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 90 primes between 38001 and 39,000, with a total of 3,467,340.
- 3
The biggest gap between neighbouring primes in this range is 42, after 38501 (the next prime is 38543). There are 11 twin prime pairs (primes 2 apart): (38237, 38239), (38327, 38329), (38447, 38449), (38459, 38461), (38567, 38569), (38609, 38611), (38651, 38653), (38669, 38671), (38711, 38713), (38747, 38749), (38921, 38923).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 38,001 to 39,000 | 90 | 9% |
Questions
How many prime numbers are there between 38001 and 39,000?
90.
What is the biggest prime number below 39,000?
38993.
What is the first prime number after 38000?
38011.