Prime numbers between 41001 and 42,000
There are 101 prime numbers between 41001 and 42,000: 41011, 41017, 41023, 41039, 41047, 41051, 41057, 41077, 41081, 41113, 41117, 41131, 41141, 41143, 41149, 41161, 41177, 41179, 41183, 41189, 41201, 41203, 41213, 41221, 41227, 41231, 41233, 41243, 41257, 41263, 41269, 41281, 41299, 41333, 41341, 41351, 41357, 41381, 41387, 41389, 41399, 41411, 41413, 41443, 41453, 41467, 41479, 41491, 41507, 41513, 41519, 41521, 41539, 41543, 41549, 41579, 41593, 41597, 41603, 41609, 41611, 41617, 41621, 41627, 41641, 41647, 41651, 41659, 41669, 41681, 41687, 41719, 41729, 41737, 41759, 41761, 41771, 41777, 41801, 41809, 41813, 41843, 41849, 41851, 41863, 41879, 41887, 41893, 41897, 41903, 41911, 41927, 41941, 41947, 41953, 41957, 41959, 41969, 41981, 41983, 41999.
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 ā42000 ā 204.9 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 101 primes between 41001 and 42,000, with a total of 4,192,173.
- 3
The biggest gap between neighbouring primes in this range is 34, after 41299 (the next prime is 41333). There are 12 twin prime pairs (primes 2 apart): (41141, 41143), (41177, 41179), (41201, 41203), (41231, 41233), (41387, 41389), (41411, 41413), (41519, 41521), (41609, 41611), (41759, 41761), (41849, 41851), (41957, 41959), (41981, 41983).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 41,001 to 42,000 | 101 | 10.1% |
Questions
How many prime numbers are there between 41001 and 42,000?
101.
What is the biggest prime number below 42,000?
41999.
What is the first prime number after 41000?
41011.