Prime numbers between 35001 and 36,000
There are 92 prime numbers between 35001 and 36,000: 35023, 35027, 35051, 35053, 35059, 35069, 35081, 35083, 35089, 35099, 35107, 35111, 35117, 35129, 35141, 35149, 35153, 35159, 35171, 35201, 35221, 35227, 35251, 35257, 35267, 35279, 35281, 35291, 35311, 35317, 35323, 35327, 35339, 35353, 35363, 35381, 35393, 35401, 35407, 35419, 35423, 35437, 35447, 35449, 35461, 35491, 35507, 35509, 35521, 35527, 35531, 35533, 35537, 35543, 35569, 35573, 35591, 35593, 35597, 35603, 35617, 35671, 35677, 35729, 35731, 35747, 35753, 35759, 35771, 35797, 35801, 35803, 35809, 35831, 35837, 35839, 35851, 35863, 35869, 35879, 35897, 35899, 35911, 35923, 35933, 35951, 35963, 35969, 35977, 35983, 35993, 35999.
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 ā36000 ā 189.7 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 92 primes between 35001 and 36,000, with a total of 3,265,954.
- 3
The biggest gap between neighbouring primes in this range is 54, after 35617 (the next prime is 35671). There are 11 twin prime pairs (primes 2 apart): (35051, 35053), (35081, 35083), (35279, 35281), (35447, 35449), (35507, 35509), (35531, 35533), (35591, 35593), (35729, 35731), (35801, 35803), (35837, 35839), (35897, 35899).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 35,001 to 36,000 | 92 | 9.2% |
Questions
How many prime numbers are there between 35001 and 36,000?
92.
What is the biggest prime number below 36,000?
35999.
What is the first prime number after 35000?
35023.