Prime or not
A prime number is a whole number greater than one whose only factors are one and itself. This checks any number, and shows the factors when there are some.
A whole number of two or more.
The first thirty primes
- 1 2
- 2 3
- 3 5
- 4 7
- 5 11
- 6 13
- 7 17
- 8 19
- 9 23
- 10 29
- 11 31
- 12 37
- 13 41
- 14 43
- 15 47
- 16 53
- 17 59
- 18 61
- 19 67
- 20 71
- 21 73
- 22 79
- 23 83
- 24 89
- 25 97
- 26 101
- 27 103
- 28 107
- 29 109
- 30 113
How many there are
Primes thin out as numbers grow, but they never run out: there is no largest prime, which Euclid proved in the Elements more than two thousand years ago. Counted with the same test this checker uses, this is how many there are below each power of ten.
| Below | Primes | Share of the numbers, rounded |
|---|---|---|
| 10 | 4 | 40% |
| 100 | 25 | 25% |
| 1,000 | 168 | 16.8% |
| 10,000 | 1,229 | 12.3% |
| 100,000 | 9,592 | 9.6% |
| 1,000,000 | 78,498 | 7.8% |
Limits
Certainty. The primality test is proven correct up to about 3.3 × 10²⁴. Past that it becomes a very good guess, so above that limit the tool says it cannot decide.
Factors. Finding the factors of a large number is far harder than deciding whether it has any, so factorising stops at fourteen digits. Past that the tool says the number is composite without listing what it divides by.