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8 | 8 | * However, there are certain numbers (so called Fermat Liars) that screw things up; |
9 | 9 | * if a is one of these liars the equation will hold even though p is composite. |
10 | 10 | * |
11 | | - * But not everything is lost! It's been proven that at least half of all integers aren't Fermat Liar (these ones called |
| 11 | + * But not everything is lost! It's been proven that at least half of all integers aren't Fermat Liars (these ones called |
12 | 12 | * Fermat Witnesses). Thus, if we keep testing the primality with random integers, we can achieve higher reliability. |
13 | 13 | * |
14 | 14 | * The interesting about all of this is that since half of all integers are Fermat Witnesses, the precision gets really |
@@ -60,14 +60,14 @@ const modularExponentiation = (base, exponent, modulus) => { |
60 | 60 | * @param {number} numberOfIterations The number of times to apply Fermat's Little Theorem |
61 | 61 | * @returns True if prime, false otherwise |
62 | 62 | */ |
63 | | -const fermatPrimeCheck = (n, numberOfIterations) => { |
64 | | - // first check for corner cases |
| 63 | +const fermatPrimeCheck = (n, numberOfIterations=50) => { |
| 64 | + // first check for edge cases |
65 | 65 | if (n <= 1 || n === 4) return false |
66 | 66 | if (n <= 3) return true // 2 and 3 are included here |
67 | 67 |
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68 | 68 | for (let i = 0; i < numberOfIterations; i++) { |
69 | | - // pick a random number between 2 and n - 2 |
70 | | - const randomNumber = Math.floor(Math.random() * (n - 1-2) + 2) |
| 69 | + // pick a random number a, with 2 <= a < n - 2 (remember Math.random() range is [0, 1[ -> 1 exclusive) |
| 70 | + const randomNumber = Math.floor(Math.random() * (n - 2) + 2) |
71 | 71 |
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72 | 72 | // if a^(n - 1) % n is different than 1, n is composite |
73 | 73 | if (modularExponentiation(randomNumber, n - 1, n) !== 1) { |
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