Prime numbers between 1 and 300
There are 62 prime numbers between 1 and 300: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293.
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 ā300 ā 17.3 (the sieve of Eratosthenes). What is left are the primes.
- 2
That leaves 62 primes between 1 and 300, with a total of 8,275.
- 3
The biggest gap between neighbouring primes in this range is 14, after 113 (the next prime is 127). There are 19 twin prime pairs (primes 2 apart), the first ones (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73).
How many primes in each part
| Range | Primes | Share of the numbers |
|---|---|---|
| 1 to 10 | 4 | 40% |
| 11 to 20 | 4 | 40% |
| 21 to 30 | 2 | 20% |
| 31 to 40 | 2 | 20% |
| 41 to 50 | 3 | 30% |
| 51 to 60 | 2 | 20% |
| 61 to 70 | 2 | 20% |
| 71 to 80 | 3 | 30% |
| 81 to 90 | 2 | 20% |
| 91 to 100 | 1 | 10% |
| 101 to 110 | 4 | 40% |
| 111 to 120 | 1 | 10% |
| 121 to 130 | 1 | 10% |
| 131 to 140 | 3 | 30% |
| 141 to 150 | 1 | 10% |
| 151 to 160 | 2 | 20% |
| 161 to 170 | 2 | 20% |
| 171 to 180 | 2 | 20% |
| 181 to 190 | 1 | 10% |
| 191 to 200 | 4 | 40% |
| 201 to 210 | 0 | 0% |
| 211 to 220 | 1 | 10% |
| 221 to 230 | 3 | 30% |
| 231 to 240 | 2 | 20% |
| 241 to 250 | 1 | 10% |
| 251 to 260 | 2 | 20% |
| 261 to 270 | 2 | 20% |
| 271 to 280 | 2 | 20% |
| 281 to 290 | 2 | 20% |
| 291 to 300 | 1 | 10% |
Questions
How many prime numbers are there between 1 and 300?
62.
What is the biggest prime number below 300?
293.
What is the first prime number after 0?
2.