Prime numbers between 2601 and 2,700
There are 15 prime numbers between 2601 and 2,700: 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699.
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 ā2700 ā 52.0 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 15 primes between 2601 and 2,700, with a total of 39,905.
- 3
The biggest gap between neighbouring primes in this range is 14, after 2633 (the next prime is 2647). There are 2 twin prime pairs (primes 2 apart): (2657, 2659), (2687, 2689).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 2,601 to 2,610 | 1 | 10% |
| 2,611 to 2,620 | 1 | 10% |
| 2,621 to 2,630 | 1 | 10% |
| 2,631 to 2,640 | 1 | 10% |
| 2,641 to 2,650 | 1 | 10% |
| 2,651 to 2,660 | 2 | 20% |
| 2,661 to 2,670 | 1 | 10% |
| 2,671 to 2,680 | 2 | 20% |
| 2,681 to 2,690 | 3 | 30% |
| 2,691 to 2,700 | 2 | 20% |
Questions
How many prime numbers are there between 2601 and 2,700?
15.
What is the biggest prime number below 2,700?
2699.
What is the first prime number after 2600?
2609.