Prime numbers between 1701 and 1,800
There are 12 prime numbers between 1701 and 1,800: 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789.
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 ā1800 ā 42.4 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 12 primes between 1701 and 1,800, with a total of 21,022.
- 3
The biggest gap between neighbouring primes in this range is 18, after 1759 (the next prime is 1777). There are 2 twin prime pairs (primes 2 apart): (1721, 1723), (1787, 1789).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 1,701 to 1,710 | 1 | 10% |
| 1,711 to 1,720 | 0 | 0% |
| 1,721 to 1,730 | 2 | 20% |
| 1,731 to 1,740 | 1 | 10% |
| 1,741 to 1,750 | 2 | 20% |
| 1,751 to 1,760 | 2 | 20% |
| 1,761 to 1,770 | 0 | 0% |
| 1,771 to 1,780 | 1 | 10% |
| 1,781 to 1,790 | 3 | 30% |
| 1,791 to 1,800 | 0 | 0% |
Questions
How many prime numbers are there between 1701 and 1,800?
12.
What is the biggest prime number below 1,800?
1789.
What is the first prime number after 1700?
1709.