# Project Euler 443
# g(10^15): jump via least prime factor of 2n-1.
import euler.nt { gcd }
function modpow(base0: i64, exp0: i64, mod: i64) -> i64 {
let mut r: i64 = 1
let mut b: i64 = base0 % mod
let mut e: i64 = exp0
while e > 0 {
if e % 2 == 1 {
let t: i128 = (r as i128) * (b as i128) % (mod as i128)
r = t as i64
}
let t2: i128 = (b as i128) * (b as i128) % (mod as i128)
b = t2 as i64
e = e / 2
}
return r
}
function is_prime_mr(n: i64) -> bool {
if n < 2 { return false }
let small: array<i64, 12> = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]
let mut i: i32 = 0
while i < 12 {
let p: i64 = small[i]
if n == p { return true }
if n % p == 0 { return false }
i = i + 1
}
let mut d: i64 = n - 1
let mut s: i32 = 0
while d % 2 == 0 {
d = d / 2
s = s + 1
}
let bases: array<i64, 7> = [2, 325, 9375, 28178, 450775, 9780504, 1795265022]
i = 0
while i < 7 {
let a: i64 = bases[i] % n
if a != 0 {
let mut x: i64 = modpow(a, d, n)
if x != 1 && x != n - 1 {
let mut r: i32 = 1
let mut ok: bool = false
while r < s {
let t: i128 = (x as i128) * (x as i128) % (n as i128)
x = t as i64
if x == n - 1 {
ok = true
break
}
r = r + 1
}
if !ok { return false }
}
}
i = i + 1
}
return true
}
function smallest_prime_factor(n0: i64) -> i64 {
if is_prime_mr(n0) { return n0 }
if n0 % 3 == 0 { return 3 }
let mut f: i64 = 5
let mut step: i64 = 2
while f * f <= n0 {
if n0 % f == 0 { return f }
f = f + step
step = 6 - step
}
return n0
}
function main() -> i32 {
let N: i64 = 1000000000000000
let mut idx: i64 = 9
let mut ans: i64 = 0
while true {
let p: i64 = smallest_prime_factor(2 * idx - 1)
let next: i64 = idx + (p - 1) / 2
if next > N {
ans = N + 2 * idx
break
}
if next == N {
ans = 3 * N
break
}
idx = next
}
printf("%lld\n", ans)
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 gcd_i64_i64(int64_t a0, int64_t b0);
int64_t lcm_i64_i64(int64_t a, int64_t b);
int64_t isqrt_i64(int64_t n);
int64_t mulmod_i64_i64_i64(int64_t a0, int64_t b0, int64_t mod);
int64_t mod_pow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod);
bool is_prime_i64(int64_t n);
int64_t modpow_i64_i64_i64(int64_t base0, int64_t exp0, int64_t mod);
bool is_prime_mr_i64(int64_t n);
int64_t smallest_prime_factor_i64(int64_t n0);
int32_t main(void);
int64_t gcd_i64_i64(int64_t a0, int64_t b0) {
int64_t a = a0;
int64_t b = b0;
while (b != 0) {
int64_t t = FLOW_CHECKED_MOD((a), (b));
a = b;
b = t;
}
return a;
}
int64_t lcm_i64_i64(int64_t a, int64_t b) {
if ((a == 0 || b == 0)) {
return 0;
}
return (FLOW_CHECKED_DIV((a), (gcd_i64_i64(a, b))) * b);
}
int64_t isqrt_i64(int64_t n) {
if (n < 2) {
return n;
}
int64_t x = n;
int64_t y = FLOW_CHECKED_DIV(((x + 1)), (2));
while (y < x) {
x = y;
y = FLOW_CHECKED_DIV(((x + FLOW_CHECKED_DIV((n), (x)))), (2));
}
return x;
}
int64_t mulmod_i64_i64_i64(int64_t a0, int64_t b0, int64_t mod) {
int64_t a = FLOW_CHECKED_MOD((a0), (mod));
int64_t b = FLOW_CHECKED_MOD((b0), (mod));
int64_t result = 0;
while (b > 0) {
if (FLOW_CHECKED_MOD((b), (2)) == 1) {
result = FLOW_CHECKED_MOD(((result + a)), (mod));
}
a = FLOW_CHECKED_MOD(((a * 2)), (mod));
b = FLOW_CHECKED_DIV((b), (2));
}
return result;
}
int64_t mod_pow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod) {
if (mod == 1) {
return 0;
}
int64_t result = 1;
int64_t b = FLOW_CHECKED_MOD((base), (mod));
int64_t e = exp;
while (e > 0) {
if (FLOW_CHECKED_MOD((e), (2)) == 1) {
result = mulmod_i64_i64_i64(result, b, mod);
}
b = mulmod_i64_i64_i64(b, b, mod);
e = FLOW_CHECKED_DIV((e), (2));
}
return result;
}
bool is_prime_i64(int64_t n) {
if (n < 2) {
return 0;
}
if (n < 4) {
return 1;
}
if ((FLOW_CHECKED_MOD((n), (2)) == 0 || FLOW_CHECKED_MOD((n), (3)) == 0)) {
return 0;
}
int64_t i = 5;
while ((i * i) <= n) {
if ((FLOW_CHECKED_MOD((n), (i)) == 0 || FLOW_CHECKED_MOD((n), ((i + 2))) == 0)) {
return 0;
}
i = (i + 6);
}
return 1;
}
int64_t modpow_i64_i64_i64(int64_t base0, int64_t exp0, int64_t mod) {
int64_t r = 1;
int64_t b = FLOW_CHECKED_MOD((base0), (mod));
int64_t e = exp0;
while (e > 0) {
if (FLOW_CHECKED_MOD((e), (2)) == 1) {
__int128 t = FLOW_CHECKED_MOD(((((__int128)(r)) * ((__int128)(b)))), (((__int128)(mod))));
r = ((int64_t)(t));
}
__int128 t2 = FLOW_CHECKED_MOD(((((__int128)(b)) * ((__int128)(b)))), (((__int128)(mod))));
b = ((int64_t)(t2));
e = FLOW_CHECKED_DIV((e), (2));
}
return r;
}
bool is_prime_mr_i64(int64_t n) {
if (n < 2) {
return 0;
}
int64_t small[12] = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 };
int32_t i = 0;
while (i < 12) {
int64_t p = (((unsigned)(i) < 12) ? small[i] : (fprintf(stderr, "array index %d out of bounds (size %d)\n", (int)(i), 12), flow_fault_handler("array index out of bounds"), small[0]));
if (n == p) {
return 1;
}
if (FLOW_CHECKED_MOD((n), (p)) == 0) {
return 0;
}
i = (i + 1);
}
int64_t d = (n - 1);
int32_t s = 0;
while (FLOW_CHECKED_MOD((d), (2)) == 0) {
d = FLOW_CHECKED_DIV((d), (2));
s = (s + 1);
}
int64_t bases[7] = { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 };
i = 0;
while (i < 7) {
int64_t a = FLOW_CHECKED_MOD(((((unsigned)(i) < 7) ? bases[i] : (fprintf(stderr, "array index %d out of bounds (size %d)\n", (int)(i), 7), flow_fault_handler("array index out of bounds"), bases[0]))), (n));
if (a != 0) {
int64_t x = modpow_i64_i64_i64(a, d, n);
if ((x != 1 && x != (n - 1))) {
int32_t r = 1;
bool ok = 0;
while (r < s) {
__int128 t = FLOW_CHECKED_MOD(((((__int128)(x)) * ((__int128)(x)))), (((__int128)(n))));
x = ((int64_t)(t));
if (x == (n - 1)) {
ok = 1;
break;
}
r = (r + 1);
}
if ((!(ok))) {
return 0;
}
}
}
i = (i + 1);
}
return 1;
}
int64_t smallest_prime_factor_i64(int64_t n0) {
if (is_prime_mr_i64(n0)) {
return n0;
}
if (FLOW_CHECKED_MOD((n0), (3)) == 0) {
return 3;
}
int64_t f = 5;
int64_t step = 2;
while ((f * f) <= n0) {
if (FLOW_CHECKED_MOD((n0), (f)) == 0) {
return f;
}
f = (f + step);
step = (6 - step);
}
return n0;
}
int32_t main(void) {
int64_t N = 1000000000000000;
int64_t idx = 9;
int64_t ans = 0;
while (1) {
int64_t p = smallest_prime_factor_i64(((2 * idx) - 1));
int64_t next = (idx + FLOW_CHECKED_DIV(((p - 1)), (2)));
if (next > N) {
ans = (N + (2 * idx));
break;
}
if (next == N) {
ans = (3 * N);
break;
}
idx = next;
}
printf("%lld\n", ans);
return 0;
}