Prime numbers between 3701 and 3,800
There are 12 prime numbers between 3701 and 3,800: 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797.
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 ā3800 ā 61.6 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 12 primes between 3701 and 3,800, with a total of 44,994.
- 3
The biggest gap between neighbouring primes in this range is 22, after 3739 (the next prime is 3761). There are 1 twin prime pairs (primes 2 apart): (3767, 3769).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 3,701 to 3,710 | 2 | 20% |
| 3,711 to 3,720 | 1 | 10% |
| 3,721 to 3,730 | 1 | 10% |
| 3,731 to 3,740 | 2 | 20% |
| 3,741 to 3,750 | 0 | 0% |
| 3,751 to 3,760 | 0 | 0% |
| 3,761 to 3,770 | 3 | 30% |
| 3,771 to 3,780 | 1 | 10% |
| 3,781 to 3,790 | 0 | 0% |
| 3,791 to 3,800 | 2 | 20% |
Questions
How many prime numbers are there between 3701 and 3,800?
12.
What is the biggest prime number below 3,800?
3797.
What is the first prime number after 3700?
3701.