Prime numbers between 77001 and 78,000
There are 95 prime numbers between 77001 and 78,000: 77003, 77017, 77023, 77029, 77041, 77047, 77069, 77081, 77093, 77101, 77137, 77141, 77153, 77167, 77171, 77191, 77201, 77213, 77237, 77239, 77243, 77249, 77261, 77263, 77267, 77269, 77279, 77291, 77317, 77323, 77339, 77347, 77351, 77359, 77369, 77377, 77383, 77417, 77419, 77431, 77447, 77471, 77477, 77479, 77489, 77491, 77509, 77513, 77521, 77527, 77543, 77549, 77551, 77557, 77563, 77569, 77573, 77587, 77591, 77611, 77617, 77621, 77641, 77647, 77659, 77681, 77687, 77689, 77699, 77711, 77713, 77719, 77723, 77731, 77743, 77747, 77761, 77773, 77783, 77797, 77801, 77813, 77839, 77849, 77863, 77867, 77893, 77899, 77929, 77933, 77951, 77969, 77977, 77983, 77999.
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 ā78000 ā 279.3 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 95 primes between 77001 and 78,000, with a total of 7,362,233.
- 3
The biggest gap between neighbouring primes in this range is 36, after 77101 (the next prime is 77137). There are 9 twin prime pairs (primes 2 apart): (77237, 77239), (77261, 77263), (77267, 77269), (77417, 77419), (77477, 77479), (77489, 77491), (77549, 77551), (77687, 77689), (77711, 77713).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 77,001 to 78,000 | 95 | 9.5% |
Questions
How many prime numbers are there between 77001 and 78,000?
95.
What is the biggest prime number below 78,000?
77999.
What is the first prime number after 77000?
77003.