Prime numbers between 68001 and 69,000
There are 80 prime numbers between 68001 and 69,000: 68023, 68041, 68053, 68059, 68071, 68087, 68099, 68111, 68113, 68141, 68147, 68161, 68171, 68207, 68209, 68213, 68219, 68227, 68239, 68261, 68279, 68281, 68311, 68329, 68351, 68371, 68389, 68399, 68437, 68443, 68447, 68449, 68473, 68477, 68483, 68489, 68491, 68501, 68507, 68521, 68531, 68539, 68543, 68567, 68581, 68597, 68611, 68633, 68639, 68659, 68669, 68683, 68687, 68699, 68711, 68713, 68729, 68737, 68743, 68749, 68767, 68771, 68777, 68791, 68813, 68819, 68821, 68863, 68879, 68881, 68891, 68897, 68899, 68903, 68909, 68917, 68927, 68947, 68963, 68993.
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 ā69000 ā 262.7 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 80 primes between 68001 and 69,000, with a total of 5,481,728.
- 3
The biggest gap between neighbouring primes in this range is 42, after 68821 (the next prime is 68863). There are 9 twin prime pairs (primes 2 apart): (68111, 68113), (68207, 68209), (68279, 68281), (68447, 68449), (68489, 68491), (68711, 68713), (68819, 68821), (68879, 68881), (68897, 68899).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 68,001 to 69,000 | 80 | 8% |
Questions
How many prime numbers are there between 68001 and 69,000?
80.
What is the biggest prime number below 69,000?
68993.
What is the first prime number after 68000?
68023.