Prime numbers between 2701 and 2,800
There are 14 prime numbers between 2701 and 2,800: 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797.
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 ā2800 ā 52.9 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 14 primes between 2701 and 2,800, with a total of 38,474.
- 3
The biggest gap between neighbouring primes in this range is 14, after 2753 (the next prime is 2767). There are 3 twin prime pairs (primes 2 apart): (2711, 2713), (2729, 2731), (2789, 2791).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 2,701 to 2,710 | 1 | 10% |
| 2,711 to 2,720 | 3 | 30% |
| 2,721 to 2,730 | 1 | 10% |
| 2,731 to 2,740 | 1 | 10% |
| 2,741 to 2,750 | 2 | 20% |
| 2,751 to 2,760 | 1 | 10% |
| 2,761 to 2,770 | 1 | 10% |
| 2,771 to 2,780 | 1 | 10% |
| 2,781 to 2,790 | 1 | 10% |
| 2,791 to 2,800 | 2 | 20% |
Questions
How many prime numbers are there between 2701 and 2,800?
14.
What is the biggest prime number below 2,800?
2797.
What is the first prime number after 2700?
2707.