Prime numbers between 3501 and 3,600
There are 14 prime numbers between 3501 and 3,600: 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593.
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 ā3600 ā 60.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 14 primes between 3501 and 3,600, with a total of 49,688.
- 3
The biggest gap between neighbouring primes in this range is 12, after 3559 (the next prime is 3571). There are 4 twin prime pairs (primes 2 apart): (3527, 3529), (3539, 3541), (3557, 3559), (3581, 3583).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 3,501 to 3,510 | 0 | 0% |
| 3,511 to 3,520 | 2 | 20% |
| 3,521 to 3,530 | 2 | 20% |
| 3,531 to 3,540 | 2 | 20% |
| 3,541 to 3,550 | 2 | 20% |
| 3,551 to 3,560 | 2 | 20% |
| 3,561 to 3,570 | 0 | 0% |
| 3,571 to 3,580 | 1 | 10% |
| 3,581 to 3,590 | 2 | 20% |
| 3,591 to 3,600 | 1 | 10% |
Questions
How many prime numbers are there between 3501 and 3,600?
14.
What is the biggest prime number below 3,600?
3593.
What is the first prime number after 3500?
3511.