Prime numbers between 3601 and 3,700
There are 13 prime numbers between 3601 and 3,700: 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697.
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 ā3700 ā 60.8 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 13 primes between 3601 and 3,700, with a total of 47,439.
- 3
The biggest gap between neighbouring primes in this range is 16, after 3643 (the next prime is 3659). There are 1 twin prime pairs (primes 2 apart): (3671, 3673).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 3,601 to 3,610 | 1 | 10% |
| 3,611 to 3,620 | 2 | 20% |
| 3,621 to 3,630 | 1 | 10% |
| 3,631 to 3,640 | 2 | 20% |
| 3,641 to 3,650 | 1 | 10% |
| 3,651 to 3,660 | 1 | 10% |
| 3,661 to 3,670 | 0 | 0% |
| 3,671 to 3,680 | 3 | 30% |
| 3,681 to 3,690 | 0 | 0% |
| 3,691 to 3,700 | 2 | 20% |
Questions
How many prime numbers are there between 3601 and 3,700?
13.
What is the biggest prime number below 3,700?
3697.
What is the first prime number after 3600?
3607.