Prime numbers between 34001 and 35,000
There are 94 prime numbers between 34001 and 35,000: 34019, 34031, 34033, 34039, 34057, 34061, 34123, 34127, 34129, 34141, 34147, 34157, 34159, 34171, 34183, 34211, 34213, 34217, 34231, 34253, 34259, 34261, 34267, 34273, 34283, 34297, 34301, 34303, 34313, 34319, 34327, 34337, 34351, 34361, 34367, 34369, 34381, 34403, 34421, 34429, 34439, 34457, 34469, 34471, 34483, 34487, 34499, 34501, 34511, 34513, 34519, 34537, 34543, 34549, 34583, 34589, 34591, 34603, 34607, 34613, 34631, 34649, 34651, 34667, 34673, 34679, 34687, 34693, 34703, 34721, 34729, 34739, 34747, 34757, 34759, 34763, 34781, 34807, 34819, 34841, 34843, 34847, 34849, 34871, 34877, 34883, 34897, 34913, 34919, 34939, 34949, 34961, 34963, 34981.
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 ā35000 ā 187.1 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 94 primes between 34001 and 35,000, with a total of 3,243,076.
- 3
The biggest gap between neighbouring primes in this range is 62, after 34061 (the next prime is 34123). There are 16 twin prime pairs (primes 2 apart), the first ones (34031, 34033), (34127, 34129), (34157, 34159), (34211, 34213), (34259, 34261), (34301, 34303), (34367, 34369), (34469, 34471).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 34,001 to 35,000 | 94 | 9.4% |
Questions
How many prime numbers are there between 34001 and 35,000?
94.
What is the biggest prime number below 35,000?
34981.
What is the first prime number after 34000?
34019.