IntIsProbablePrime

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API Reference

IntIsProbablePrime

Description

Test whether the integer is probably prime using a Miller-Rabin style primality check.

This public macro supports both forms:

IntIsProbablePrime(value) - returns the result, no error channel.
IntIsProbablePrime(value, error) - writes the error flag through error.

Parameters

Name	Direction	Description
`value`	in	Integer to test.
`error`	out	Optional pointer set to `true` on internal failure and `false` on success.

Success

Returns true when the value is probably prime.

Failure

Returns false for composite values. With the two-argument form, *error is set to true on internal allocation failure during the witness loop and false otherwise.

Usage example (Cross-references)

Usage examples (Cross-references)

In Int.c:2790:

        {
            bool prime_error = false;
            bool prime       = IntIsProbablePrime(modulus, &prime_error);
    
            if (prime_error) {

In Math.c:882:

    
    bool test_int_is_probable_prime(void) {
        WriteFmt("Testing IntIsProbablePrime\n");
    
        DefaultAllocator alloc = DefaultAllocatorInit();

In Math.c:889:

        Int composite = IntFrom(561, &alloc.base);
    
        bool result = IntIsProbablePrime(&prime);
        result      = result && !IntIsProbablePrime(&composite);

In Math.c:890:

    
        bool result = IntIsProbablePrime(&prime);
        result      = result && !IntIsProbablePrime(&composite);
    
        IntDeinit(&prime);

In Math.c:3000:

    
    bool test_m4_one_not_prime(void) {
        WriteFmt("Testing IntIsProbablePrime(1) == false\n");
    
        DefaultAllocator alloc = DefaultAllocatorInit();

In Math.c:3006:

        Int value = IntFrom(1, &alloc.base);
    
        bool result = !IntIsProbablePrime(&value);
    
        IntDeinit(&value);

In Math.c:3014:

    
    bool test_m4_two_is_prime(void) {
        WriteFmt("Testing IntIsProbablePrime(2) == true\n");
    
        DefaultAllocator alloc = DefaultAllocatorInit();

In Math.c:3020:

        Int value = IntFrom(2, &alloc.base);
    
        bool result = IntIsProbablePrime(&value);
    
        IntDeinit(&value);

In Math.c:3028:

    
    bool test_m4_four_not_prime(void) {
        WriteFmt("Testing IntIsProbablePrime(4) == false\n");
    
        DefaultAllocator alloc = DefaultAllocatorInit();

In Math.c:3034:

        Int value = IntFrom(4, &alloc.base);
    
        bool result = !IntIsProbablePrime(&value);
    
        IntDeinit(&value);

In Math.c:3042:

    
    bool test_m4_three_is_prime(void) {
        WriteFmt("Testing IntIsProbablePrime(3) == true\n");
    
        DefaultAllocator alloc = DefaultAllocatorInit();

In Math.c:3048:

        Int value = IntFrom(3, &alloc.base);
    
        bool result = IntIsProbablePrime(&value);
    
        IntDeinit(&value);

In Math.c:3056:

    
    bool test_m4_prime_97(void) {
        WriteFmt("Testing IntIsProbablePrime(97) == true (deep witness loop)\n");
    
        DefaultAllocator alloc = DefaultAllocatorInit();

In Math.c:3062:

        Int value = IntFrom(97, &alloc.base);
    
        bool result = IntIsProbablePrime(&value);
    
        IntDeinit(&value);

In Math.c:3070:

    
    bool test_m4_composite_561(void) {
        WriteFmt("Testing IntIsProbablePrime(561) == false (Carmichael)\n");
    
        DefaultAllocator alloc = DefaultAllocatorInit();

In Math.c:3076:

        Int value = IntFrom(561, &alloc.base);
    
        bool result = !IntIsProbablePrime(&value);
    
        IntDeinit(&value);

In Math.c:3084:

    
    bool test_m4_composite_1763(void) {
        WriteFmt("Testing IntIsProbablePrime(1763 = 41*43) == false (reaches MR)\n");
    
        DefaultAllocator alloc = DefaultAllocatorInit();

In Math.c:3090:

        Int value = IntFrom(1763, &alloc.base);
    
        bool result = !IntIsProbablePrime(&value);
    
        IntDeinit(&value);

In Math.c:3098:

    
    bool test_m4_spsp_1373653_composite(void) {
        WriteFmt("Testing IntIsProbablePrime(1373653) == false (SPSP base 2,3)\n");
    
        DefaultAllocator alloc = DefaultAllocatorInit();

In Math.c:3104:

        Int value = IntFromStr("1373653", &alloc.base);
    
        bool result = !IntIsProbablePrime(&value);
    
        IntDeinit(&value);

In Math.c:3112:

    
    bool test_m4_large_prime(void) {
        WriteFmt("Testing IntIsProbablePrime(1000000007) == true\n");
    
        DefaultAllocator alloc = DefaultAllocatorInit();

In Math.c:3118:

        Int value = IntFromStr("1000000007", &alloc.base);
    
        bool result = IntIsProbablePrime(&value);
    
        IntDeinit(&value);

In Math.c:3126:

    
    bool test_m4_error_flag_cleared(void) {
        WriteFmt("Testing IntIsProbablePrime clears the error flag\n");
    
        DefaultAllocator alloc = DefaultAllocatorInit();

In Math.c:3133:

        bool error = true;
    
        bool prime  = IntIsProbablePrime(&value, &error);
        bool result = prime && !error;

In Math.c:4582:

        Int composite = IntFrom(1000005u, a); // composite
    
        bool ok = IntIsProbablePrime(&prime) && !IntIsProbablePrime(&composite);
    
        IntDeinit(&prime);

In Math.c:4600:

        Int n = IntFrom(2047u, a);
    
        bool ok = !IntIsProbablePrime(&n);
    
        IntDeinit(&n);

In Math.c:4845:

        Int  value = IntFrom(561u, alloc);
        bool error = false;
        bool prime = IntIsProbablePrime(&value, &error);
        bool ok    = (error == false) && (prime == false);

Last updated on July 1, 2026

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