Prime numbers between 78001 and 79,000
There are 84 prime numbers between 78001 and 79,000: 78007, 78017, 78031, 78041, 78049, 78059, 78079, 78101, 78121, 78137, 78139, 78157, 78163, 78167, 78173, 78179, 78191, 78193, 78203, 78229, 78233, 78241, 78259, 78277, 78283, 78301, 78307, 78311, 78317, 78341, 78347, 78367, 78401, 78427, 78437, 78439, 78467, 78479, 78487, 78497, 78509, 78511, 78517, 78539, 78541, 78553, 78569, 78571, 78577, 78583, 78593, 78607, 78623, 78643, 78649, 78653, 78691, 78697, 78707, 78713, 78721, 78737, 78779, 78781, 78787, 78791, 78797, 78803, 78809, 78823, 78839, 78853, 78857, 78877, 78887, 78889, 78893, 78901, 78919, 78929, 78941, 78977, 78979, 78989.
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 ā79000 ā 281.1 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 84 primes between 78001 and 79,000, with a total of 6,594,258.
- 3
The biggest gap between neighbouring primes in this range is 42, after 78737 (the next prime is 78779). There are 9 twin prime pairs (primes 2 apart): (78137, 78139), (78191, 78193), (78437, 78439), (78509, 78511), (78539, 78541), (78569, 78571), (78779, 78781), (78887, 78889), (78977, 78979).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 78,001 to 79,000 | 84 | 8.4% |
Questions
How many prime numbers are there between 78001 and 79,000?
84.
What is the biggest prime number below 79,000?
78989.
What is the first prime number after 78000?
78007.