Prime numbers between 1801 and 1,900
There are 12 prime numbers between 1801 and 1,900: 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889.
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 ā1900 ā 43.6 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 12 primes between 1801 and 1,900, with a total of 22,230.
- 3
The biggest gap between neighbouring primes in this range is 16, after 1831 (the next prime is 1847). There are 2 twin prime pairs (primes 2 apart): (1871, 1873), (1877, 1879).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 1,801 to 1,810 | 1 | 10% |
| 1,811 to 1,820 | 1 | 10% |
| 1,821 to 1,830 | 1 | 10% |
| 1,831 to 1,840 | 1 | 10% |
| 1,841 to 1,850 | 1 | 10% |
| 1,851 to 1,860 | 0 | 0% |
| 1,861 to 1,870 | 2 | 20% |
| 1,871 to 1,880 | 4 | 40% |
| 1,881 to 1,890 | 1 | 10% |
| 1,891 to 1,900 | 0 | 0% |
Questions
How many prime numbers are there between 1801 and 1,900?
12.
What is the biggest prime number below 1,900?
1889.
What is the first prime number after 1800?
1801.