Prime numbers between 7701 and 7,800
There are 10 prime numbers between 7701 and 7,800: 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793.
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 ā7800 ā 88.3 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 10 primes between 7701 and 7,800, with a total of 77,462.
- 3
The biggest gap between neighbouring primes in this range is 30, after 7759 (the next prime is 7789). There are 1 twin prime pairs (primes 2 apart): (7757, 7759).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 7,701 to 7,710 | 1 | 10% |
| 7,711 to 7,720 | 1 | 10% |
| 7,721 to 7,730 | 2 | 20% |
| 7,731 to 7,740 | 0 | 0% |
| 7,741 to 7,750 | 1 | 10% |
| 7,751 to 7,760 | 3 | 30% |
| 7,761 to 7,770 | 0 | 0% |
| 7,771 to 7,780 | 0 | 0% |
| 7,781 to 7,790 | 1 | 10% |
| 7,791 to 7,800 | 1 | 10% |
Questions
How many prime numbers are there between 7701 and 7,800?
10.
What is the biggest prime number below 7,800?
7793.
What is the first prime number after 7700?
7703.