Prime numbers between 42001 and 43,000
There are 102 prime numbers between 42001 and 43,000: 42013, 42017, 42019, 42023, 42043, 42061, 42071, 42073, 42083, 42089, 42101, 42131, 42139, 42157, 42169, 42179, 42181, 42187, 42193, 42197, 42209, 42221, 42223, 42227, 42239, 42257, 42281, 42283, 42293, 42299, 42307, 42323, 42331, 42337, 42349, 42359, 42373, 42379, 42391, 42397, 42403, 42407, 42409, 42433, 42437, 42443, 42451, 42457, 42461, 42463, 42467, 42473, 42487, 42491, 42499, 42509, 42533, 42557, 42569, 42571, 42577, 42589, 42611, 42641, 42643, 42649, 42667, 42677, 42683, 42689, 42697, 42701, 42703, 42709, 42719, 42727, 42737, 42743, 42751, 42767, 42773, 42787, 42793, 42797, 42821, 42829, 42839, 42841, 42853, 42859, 42863, 42899, 42901, 42923, 42929, 42937, 42943, 42953, 42961, 42967, 42979, 42989.
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 ā43000 ā 207.4 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 102 primes between 42001 and 43,000, with a total of 4,334,840.
- 3
The biggest gap between neighbouring primes in this range is 36, after 42863 (the next prime is 42899). There are 12 twin prime pairs (primes 2 apart): (42017, 42019), (42071, 42073), (42179, 42181), (42221, 42223), (42281, 42283), (42407, 42409), (42461, 42463), (42569, 42571), (42641, 42643), (42701, 42703), (42839, 42841), (42899, 42901).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 42,001 to 43,000 | 102 | 10.2% |
Questions
How many prime numbers are there between 42001 and 43,000?
102.
What is the biggest prime number below 43,000?
42989.
What is the first prime number after 42000?
42013.