# Project Euler 133
# Sum of primes below 100000 that never divide R(10^k).
function mod_pow(base: i64, exp: i64, mod: i64) -> i64 {
let mut r: i64 = 1
let mut b: i64 = base % mod
let mut e: i64 = exp
while e > 0 {
if e % 2 == 1 { r = (r * b) % mod }
b = (b * b) % mod
e = e / 2
}
return r
}
function divides_some_R10k(p: i64) -> bool {
# 2,3,5 never divide R(10^n): 2/5 end in 1; R(10^n) ≡ 1 (mod 3).
if p == 2 || p == 3 || p == 5 { return false }
# multiplicative order of 10 modulo p
let mut ord: i64 = p - 1
let mut n: i64 = p - 1
let mut f: i64 = 2
while f * f <= n {
if n % f == 0 {
while n % f == 0 { n = n / f }
while ord % f == 0 && mod_pow(10, ord / f, p) == 1 {
ord = ord / f
}
}
f = f + 1
}
if n > 1 {
while ord % n == 0 && mod_pow(10, ord / n, p) == 1 {
ord = ord / n
}
}
while ord % 2 == 0 { ord = ord / 2 }
while ord % 5 == 0 { ord = ord / 5 }
return ord == 1
}
function main() -> i32 {
let mut total: i64 = 0
let mut n: i64 = 2
while n < 100000 {
let mut prime: bool = true
if n >= 4 && n % 2 == 0 { prime = false }
let mut d: i64 = 3
while prime && d * d <= n {
if n % d == 0 { prime = false }
d = d + 2
}
if prime {
if !divides_some_R10k(n) {
total = total + n
}
}
n = n + 1
}
printf("%lld\n", total)
return 0
}
Generated C
#include <stdint.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
/* Flow runtime helpers */
typedef struct flow_temp_node { struct flow_temp_node* next; } flow_temp_node;
static flow_temp_node* flow_temp_head = NULL;
static int flow_temp_atexit_set = 0;
__attribute__((unused)) static void flow_temp_free_all(void) {
while (flow_temp_head) {
flow_temp_node* n = flow_temp_head;
flow_temp_head = n->next;
free(n);
}
}
__attribute__((unused)) static void* flow_temp_alloc(size_t nbytes) {
flow_temp_node* node = (flow_temp_node*)malloc(sizeof(flow_temp_node) + nbytes);
if (!node) return NULL;
node->next = flow_temp_head;
flow_temp_head = node;
if (!flow_temp_atexit_set) {
flow_temp_atexit_set = 1;
atexit(flow_temp_free_all);
}
return (void*)(node + 1);
}
#ifndef FLOW_DIAG
#define FLOW_DIAG(msg) fprintf(stderr, "%s", (msg))
#endif
#ifndef FLOW_LOG
#define FLOW_LOG(fmt, ...) printf(fmt, __VA_ARGS__)
#endif
#ifndef FLOW_LOG_EMPTY
#define FLOW_LOG_EMPTY(fmt) printf(fmt)
#endif
static char* flow_strcat(const char* a, const char* b) {
size_t la = strlen(a ? a : ""), lb = strlen(b ? b : "");
char* r = (char*)flow_temp_alloc(la + lb + 1);
if (!r) return NULL;
if (la) memcpy(r, a, la);
if (lb) memcpy(r + la, b, lb);
r[la + lb] = '\0';
return r;
}
#define __flow_in_arr(arr, val) __extension__ ({ \
int _found = 0; \
size_t _n = sizeof(arr)/sizeof((arr)[0]); \
for (size_t _i = 0; _i < _n; _i++) { \
if ((arr)[_i] == (val)) { _found = 1; break; } \
} _found; })
/* Unified fault handler (MISRA #279) — override with -DFLOW_FAULT_HANDLER=fn */
#ifndef FLOW_FAULT_HANDLER
__attribute__((unused)) static inline void flow_fault_handler(const char* msg) {
fprintf(stderr, "flow: %s\n", msg ? msg : "fault");
abort();
#if defined(__GNUC__) || defined(__clang__)
__builtin_unreachable();
#endif
}
#else
#define flow_fault_handler FLOW_FAULT_HANDLER
#endif
#define flow_div_by_zero_handler() flow_fault_handler("division by zero")
#define flow_shift_ub_handler() flow_fault_handler("invalid shift (amount out of range or left-shift of negative)")
#ifndef FLOW_CHECKED_DIV
#define FLOW_CHECKED_DIV(L, R) (((R) != 0) ? ((L) / (R)) : (flow_div_by_zero_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_MOD
#define FLOW_CHECKED_MOD(L, R) (((R) != 0) ? ((L) % (R)) : (flow_div_by_zero_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_SHL
#define FLOW_CHECKED_SHL(L, R) ((((R) >= 0) && ((unsigned long long)(R) < (sizeof(L) * 8ull)) && ((L) >= 0)) ? ((L) << (R)) : (flow_shift_ub_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_SHR
#define FLOW_CHECKED_SHR(L, R) ((((R) >= 0) && ((unsigned long long)(R) < (sizeof(L) * 8ull))) ? ((L) >> (R)) : (flow_shift_ub_handler(), (L) * 0))
#endif
#include <math.h>
void* _ui_state = NULL;
static inline float i32_to_f32(int32_t v) { return (float)v; }
/* Host stub for @gpu kernels (device codegen replaces this). */
static inline int32_t gpu_thread_id(void) { return 0; }
int64_t mod_pow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod);
bool divides_some_R10k_i64(int64_t p);
int32_t main(void);
int64_t mod_pow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod) {
int64_t r = 1;
int64_t b = FLOW_CHECKED_MOD((base), (mod));
int64_t e = exp;
while (e > 0) {
if (FLOW_CHECKED_MOD((e), (2)) == 1) {
r = FLOW_CHECKED_MOD(((r * b)), (mod));
}
b = FLOW_CHECKED_MOD(((b * b)), (mod));
e = FLOW_CHECKED_DIV((e), (2));
}
return r;
}
bool divides_some_R10k_i64(int64_t p) {
if (((p == 2 || p == 3) || p == 5)) {
return 0;
}
int64_t ord = (p - 1);
int64_t n = (p - 1);
int64_t f = 2;
while ((f * f) <= n) {
if (FLOW_CHECKED_MOD((n), (f)) == 0) {
while (FLOW_CHECKED_MOD((n), (f)) == 0) {
n = FLOW_CHECKED_DIV((n), (f));
}
while ((FLOW_CHECKED_MOD((ord), (f)) == 0 && mod_pow_i64_i64_i64(10, FLOW_CHECKED_DIV((ord), (f)), p) == 1)) {
ord = FLOW_CHECKED_DIV((ord), (f));
}
}
f = (f + 1);
}
if (n > 1) {
while ((FLOW_CHECKED_MOD((ord), (n)) == 0 && mod_pow_i64_i64_i64(10, FLOW_CHECKED_DIV((ord), (n)), p) == 1)) {
ord = FLOW_CHECKED_DIV((ord), (n));
}
}
while (FLOW_CHECKED_MOD((ord), (2)) == 0) {
ord = FLOW_CHECKED_DIV((ord), (2));
}
while (FLOW_CHECKED_MOD((ord), (5)) == 0) {
ord = FLOW_CHECKED_DIV((ord), (5));
}
return ord == 1;
}
int32_t main(void) {
int64_t total = 0;
int64_t n = 2;
while (n < 100000) {
bool prime = 1;
if ((n >= 4 && FLOW_CHECKED_MOD((n), (2)) == 0)) {
prime = 0;
}
int64_t d = 3;
while ((prime && (d * d) <= n)) {
if (FLOW_CHECKED_MOD((n), (d)) == 0) {
prime = 0;
}
d = (d + 2);
}
if (prime) {
if ((!(divides_some_R10k_i64(n)))) {
total = (total + n);
}
}
n = (n + 1);
}
printf("%lld\n", total);
return 0;
}