Prime numbers between 69001 and 70,000
There are 81 prime numbers between 69001 and 70,000: 69001, 69011, 69019, 69029, 69031, 69061, 69067, 69073, 69109, 69119, 69127, 69143, 69149, 69151, 69163, 69191, 69193, 69197, 69203, 69221, 69233, 69239, 69247, 69257, 69259, 69263, 69313, 69317, 69337, 69341, 69371, 69379, 69383, 69389, 69401, 69403, 69427, 69431, 69439, 69457, 69463, 69467, 69473, 69481, 69491, 69493, 69497, 69499, 69539, 69557, 69593, 69623, 69653, 69661, 69677, 69691, 69697, 69709, 69737, 69739, 69761, 69763, 69767, 69779, 69809, 69821, 69827, 69829, 69833, 69847, 69857, 69859, 69877, 69899, 69911, 69929, 69931, 69941, 69959, 69991, 69997.
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 ā70000 ā 264.6 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 81 primes between 69001 and 70,000, with a total of 5,628,071.
- 3
The biggest gap between neighbouring primes in this range is 50, after 69263 (the next prime is 69313). There are 12 twin prime pairs (primes 2 apart): (69029, 69031), (69149, 69151), (69191, 69193), (69257, 69259), (69401, 69403), (69491, 69493), (69497, 69499), (69737, 69739), (69761, 69763), (69827, 69829), (69857, 69859), (69929, 69931).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 69,001 to 70,000 | 81 | 8.1% |
Questions
How many prime numbers are there between 69001 and 70,000?
81.
What is the biggest prime number below 70,000?
69997.
What is the first prime number after 69000?
69001.