Prime numbers between 801 and 900
There are 15 prime numbers between 801 and 900: 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887.
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 ā900 ā 30.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 15 primes between 801 and 900, with a total of 12,719.
- 3
The biggest gap between neighbouring primes in this range is 14, after 839 (the next prime is 853). There are 5 twin prime pairs (primes 2 apart): (809, 811), (821, 823), (827, 829), (857, 859), (881, 883).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 801 to 810 | 1 | 10% |
| 811 to 820 | 1 | 10% |
| 821 to 830 | 4 | 40% |
| 831 to 840 | 1 | 10% |
| 841 to 850 | 0 | 0% |
| 851 to 860 | 3 | 30% |
| 861 to 870 | 1 | 10% |
| 871 to 880 | 1 | 10% |
| 881 to 890 | 3 | 30% |
| 891 to 900 | 0 | 0% |
Questions
How many prime numbers are there between 801 and 900?
15.
What is the biggest prime number below 900?
887.
What is the first prime number after 800?
809.