Prime numbers between 601 and 700
There are 16 prime numbers between 601 and 700: 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691.
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 ā700 ā 26.5 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 16 primes between 601 and 700, with a total of 10,316.
- 3
The biggest gap between neighbouring primes in this range is 12, after 619 (the next prime is 631). There are 3 twin prime pairs (primes 2 apart): (617, 619), (641, 643), (659, 661).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 601 to 610 | 2 | 20% |
| 611 to 620 | 3 | 30% |
| 621 to 630 | 0 | 0% |
| 631 to 640 | 1 | 10% |
| 641 to 650 | 3 | 30% |
| 651 to 660 | 2 | 20% |
| 661 to 670 | 1 | 10% |
| 671 to 680 | 2 | 20% |
| 681 to 690 | 1 | 10% |
| 691 to 700 | 1 | 10% |
Questions
How many prime numbers are there between 601 and 700?
16.
What is the biggest prime number below 700?
691.
What is the first prime number after 600?
601.