Prime numbers between 2501 and 2,600
There are 11 prime numbers between 2501 and 2,600: 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593.
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 ā2600 ā 51.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 11 primes between 2501 and 2,600, with a total of 28,057.
- 3
The biggest gap between neighbouring primes in this range is 22, after 2557 (the next prime is 2579). There are 2 twin prime pairs (primes 2 apart): (2549, 2551), (2591, 2593).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 2,501 to 2,510 | 1 | 10% |
| 2,511 to 2,520 | 0 | 0% |
| 2,521 to 2,530 | 1 | 10% |
| 2,531 to 2,540 | 2 | 20% |
| 2,541 to 2,550 | 2 | 20% |
| 2,551 to 2,560 | 2 | 20% |
| 2,561 to 2,570 | 0 | 0% |
| 2,571 to 2,580 | 1 | 10% |
| 2,581 to 2,590 | 0 | 0% |
| 2,591 to 2,600 | 2 | 20% |
Questions
How many prime numbers are there between 2501 and 2,600?
11.
What is the biggest prime number below 2,600?
2593.
What is the first prime number after 2500?
2503.