Prime numbers between 29001 and 30,000
There are 92 prime numbers between 29001 and 30,000: 29009, 29017, 29021, 29023, 29027, 29033, 29059, 29063, 29077, 29101, 29123, 29129, 29131, 29137, 29147, 29153, 29167, 29173, 29179, 29191, 29201, 29207, 29209, 29221, 29231, 29243, 29251, 29269, 29287, 29297, 29303, 29311, 29327, 29333, 29339, 29347, 29363, 29383, 29387, 29389, 29399, 29401, 29411, 29423, 29429, 29437, 29443, 29453, 29473, 29483, 29501, 29527, 29531, 29537, 29567, 29569, 29573, 29581, 29587, 29599, 29611, 29629, 29633, 29641, 29663, 29669, 29671, 29683, 29717, 29723, 29741, 29753, 29759, 29761, 29789, 29803, 29819, 29833, 29837, 29851, 29863, 29867, 29873, 29879, 29881, 29917, 29921, 29927, 29947, 29959, 29983, 29989.
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 ā30000 ā 173.2 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 92 primes between 29001 and 30,000, with a total of 2,711,374.
- 3
The biggest gap between neighbouring primes in this range is 36, after 29881 (the next prime is 29917). There are 9 twin prime pairs (primes 2 apart): (29021, 29023), (29129, 29131), (29207, 29209), (29387, 29389), (29399, 29401), (29567, 29569), (29669, 29671), (29759, 29761), (29879, 29881).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 29,001 to 30,000 | 92 | 9.2% |
Questions
How many prime numbers are there between 29001 and 30,000?
92.
What is the biggest prime number below 30,000?
29989.
What is the first prime number after 29000?
29009.