Prime numbers between 1901 and 2,000
There are 13 prime numbers between 1901 and 2,000: 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999.
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 ā2000 ā 44.7 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 13 primes between 1901 and 2,000, with a total of 25,413.
- 3
The biggest gap between neighbouring primes in this range is 22, after 1951 (the next prime is 1973). There are 3 twin prime pairs (primes 2 apart): (1931, 1933), (1949, 1951), (1997, 1999).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 1,901 to 1,910 | 2 | 20% |
| 1,911 to 1,920 | 1 | 10% |
| 1,921 to 1,930 | 0 | 0% |
| 1,931 to 1,940 | 2 | 20% |
| 1,941 to 1,950 | 1 | 10% |
| 1,951 to 1,960 | 1 | 10% |
| 1,961 to 1,970 | 0 | 0% |
| 1,971 to 1,980 | 2 | 20% |
| 1,981 to 1,990 | 1 | 10% |
| 1,991 to 2,000 | 3 | 30% |
Questions
How many prime numbers are there between 1901 and 2,000?
13.
What is the biggest prime number below 2,000?
1999.
What is the first prime number after 1900?
1901.