A composite integer has a factor no larger than its square root.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 | "use strict"; // Trial Division Primality in JavaScript // // PURPOSE // A composite integer has a factor no larger than its square root. Trial division checks // only candidate divisors up to that bound. // // METHOD // Reject values below two, handle two, and reject other even values. Test odd divisors until // d exceeds n/d, which avoids computing d squared. // // COMPLEXITY // O(sqrt(n)) time and O(1) auxiliary space. // // CONTRACT // Returns 1 for prime, 0 otherwise. This is suitable for small integers, not large // cryptographic candidates. // Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex // counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers. // Sorted order, correct tree topology, and caller-owned data-structure invariants are // preconditions; checking them on every query would change query complexity. // Scalar and shape checks are included. Value-range checks are included where needed to // prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000 // workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python // uses arbitrary precision. Native allocation failures propagate. In-place outputs may be // partly updated after arithmetic failure. These are single-threaded, in-memory // implementations. // // LANGUAGE DETAILS // Node.js 18+: Int32Array inputs and workspaces provide compact integer storage. Automatic // lengths and checked arithmetic reject values outside signed 32-bit. Invalid inputs or // overflow throw RangeError. // // EXAMPLE // Expected return: 1. // Run: node example.js // Tests for this exact source artifact run before publication. The accompanying source // archive includes unit cases, runtime results, and source hashes. function alg_require(valid) { if (!valid) throw new RangeError("invalid algorithm input"); } function alg_checked(v) { if (!Number.isInteger(v) || v < -2147483648 || v > 2147483647) throw new RangeError("32-bit result overflow"); return v; } function alg_add(a,b) { return alg_checked(a+b); } function alg_sub(a,b) { return alg_checked(a-b); } function alg_mul(a,b) { return alg_checked(a*b); } function alg_size(n) { alg_require(Number.isInteger(n) && n>=0 && n<=4000000); return n; } function is_prime(n) { alg_require(Number.isInteger(n) && n >= -2147483648 && n <= 2147483647); if ((n < 2)) { return 0; } if ((n == 2)) { return 1; } if (((n % 2) == 0)) { return 0; } let d = 3; while ((d <= Math.floor(n / d))) { if (((n % d) == 0)) { return 0; } d = alg_add(d, 2); } return 1; } let n = 97; let result = is_prime(n); console.log(result); |