Prime numbers between 701 and 800
There are 14 prime numbers between 701 and 800: 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797.
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 ā800 ā 28.3 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 14 primes between 701 and 800, with a total of 10,466.
- 3
The biggest gap between neighbouring primes in this range is 14, after 773 (the next prime is 787). There are no twin primes here.
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 701 to 710 | 2 | 20% |
| 711 to 720 | 1 | 10% |
| 721 to 730 | 1 | 10% |
| 731 to 740 | 2 | 20% |
| 741 to 750 | 1 | 10% |
| 751 to 760 | 2 | 20% |
| 761 to 770 | 2 | 20% |
| 771 to 780 | 1 | 10% |
| 781 to 790 | 1 | 10% |
| 791 to 800 | 1 | 10% |
Questions
How many prime numbers are there between 701 and 800?
14.
What is the biggest prime number below 800?
797.
What is the first prime number after 700?
701.