Prime numbers between 49001 and 50,000
There are 98 prime numbers between 49001 and 50,000: 49003, 49009, 49019, 49031, 49033, 49037, 49043, 49057, 49069, 49081, 49103, 49109, 49117, 49121, 49123, 49139, 49157, 49169, 49171, 49177, 49193, 49199, 49201, 49207, 49211, 49223, 49253, 49261, 49277, 49279, 49297, 49307, 49331, 49333, 49339, 49363, 49367, 49369, 49391, 49393, 49409, 49411, 49417, 49429, 49433, 49451, 49459, 49463, 49477, 49481, 49499, 49523, 49529, 49531, 49537, 49547, 49549, 49559, 49597, 49603, 49613, 49627, 49633, 49639, 49663, 49667, 49669, 49681, 49697, 49711, 49727, 49739, 49741, 49747, 49757, 49783, 49787, 49789, 49801, 49807, 49811, 49823, 49831, 49843, 49853, 49871, 49877, 49891, 49919, 49921, 49927, 49937, 49939, 49943, 49957, 49991, 49993, 49999.
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 ā50000 ā 223.6 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 98 primes between 49001 and 50,000, with a total of 4,850,070.
- 3
The biggest gap between neighbouring primes in this range is 38, after 49559 (the next prime is 49597). There are 17 twin prime pairs (primes 2 apart), the first ones (49031, 49033), (49121, 49123), (49169, 49171), (49199, 49201), (49277, 49279), (49331, 49333), (49367, 49369), (49391, 49393).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 49,001 to 50,000 | 98 | 9.8% |
Questions
How many prime numbers are there between 49001 and 50,000?
98.
What is the biggest prime number below 50,000?
49999.
What is the first prime number after 49000?
49003.