Prime numbers between 1601 and 1,700
There are 15 prime numbers between 1601 and 1,700: 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699.
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 ā1700 ā 41.2 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 15 primes between 1601 and 1,700, with a total of 24,679.
- 3
The biggest gap between neighbouring primes in this range is 24, after 1669 (the next prime is 1693). There are 4 twin prime pairs (primes 2 apart): (1607, 1609), (1619, 1621), (1667, 1669), (1697, 1699).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 1,601 to 1,610 | 3 | 30% |
| 1,611 to 1,620 | 2 | 20% |
| 1,621 to 1,630 | 2 | 20% |
| 1,631 to 1,640 | 1 | 10% |
| 1,641 to 1,650 | 0 | 0% |
| 1,651 to 1,660 | 1 | 10% |
| 1,661 to 1,670 | 3 | 30% |
| 1,671 to 1,680 | 0 | 0% |
| 1,681 to 1,690 | 0 | 0% |
| 1,691 to 1,700 | 3 | 30% |
Questions
How many prime numbers are there between 1601 and 1,700?
15.
What is the biggest prime number below 1,700?
1699.
What is the first prime number after 1600?
1601.