# Project Euler 421
# sum_{n=1..10^11} s(n,10^8) where s sums prime factors of n^15+1 <= 10^8.
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
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 {
r = ((r as i128) * (b as i128) % (mod as i128)) as i64
}
b = ((b as i128) * (b as i128) % (mod as i128)) as i64
e = e / 2
}
return r
}
function is_order_15(g: i64, p: i64) -> i64 {
if g == 1 { return 0 }
let g2: i64 = ((g as i128) * (g as i128) % (p as i128)) as i64
let g3: i64 = ((g2 as i128) * (g as i128) % (p as i128)) as i64
if g3 == 1 { return 0 }
let g5: i64 = ((g2 as i128) * (g3 as i128) % (p as i128)) as i64
if g5 == 1 { return 0 }
return 1
}
function find_gen(p: i64, d: i64) -> i64 {
let exp: i64 = (p - 1) / d
let bases: ptr<i64> = calloc(30, 8)
let nb: i64 = 25
bases[0]=2; bases[1]=3; bases[2]=5; bases[3]=7; bases[4]=11
bases[5]=13; bases[6]=17; bases[7]=19; bases[8]=23; bases[9]=29
bases[10]=31; bases[11]=37; bases[12]=41; bases[13]=43; bases[14]=47
bases[15]=53; bases[16]=59; bases[17]=61; bases[18]=67; bases[19]=71
bases[20]=73; bases[21]=79; bases[22]=83; bases[23]=89; bases[24]=97
let mut i: i64 = 0
while i < nb {
let a: i64 = bases[i]
if a >= p { break }
let g: i64 = modpow(a, exp, p)
if d == 3 || d == 5 {
if g != 1 { free(bases); return g }
} else {
if is_order_15(g, p) == 1 { free(bases); return g }
}
i = i + 1
}
let mut a2: i64 = 2
while a2 < p && a2 < 500 {
let g2: i64 = modpow(a2, exp, p)
if d == 3 || d == 5 {
if g2 != 1 { free(bases); return g2 }
} else {
if is_order_15(g2, p) == 1 { free(bases); return g2 }
}
a2 = a2 + 1
}
free(bases)
return 1
}
function main() -> i32 {
let L: i64 = 100000000000
let M: i64 = 100000000
let size: i64 = M / 2 + 1
let odd: ptr<i8> = calloc(size, 1)
if odd == null { return 1 }
let mut i: i64 = 0
while i < size { odd[i] = 1; i = i + 1 }
odd[0] = 0
let mut p: i64 = 3
while p * p <= M {
if odd[p >> 1] != 0 {
let mut cur: i64 = (p * p) >> 1
while cur < size {
odd[cur] = 0
cur = cur + p
}
}
p = p + 2
}
let d_table: ptr<i32> = calloc(30, 4)
i = 0
while i < 30 { d_table[i] = 1; i = i + 1 }
d_table[1] = 15
d_table[11] = 5
d_table[7] = 3
d_table[13] = 3
d_table[19] = 3
let mut ans: i64 = 2 * ((L + 1) / 2)
p = 3
while p <= M {
if odd[p >> 1] != 0 {
let d: i64 = d_table[p % 30] as i64
let q: i64 = L / p
let t: i64 = L % p
if d == 1 {
let mut cnt: i64 = q
if t == p - 1 { cnt = cnt + 1 }
ans = ans + p * cnt
} else {
let g: i64 = find_gen(p, d)
let threshold: i64 = p - t
let mut u: i64 = 1
let mut extra: i64 = 0
let mut k: i64 = 0
while k < d {
if u >= threshold { extra = extra + 1 }
u = ((u as i128) * (g as i128) % (p as i128)) as i64
k = k + 1
}
ans = ans + p * (d * q + extra)
}
}
p = p + 2
}
printf("%lld\n", ans)
free(d_table)
free(odd)
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 modpow_i64_i64_i64(int64_t base0, int64_t exp0, int64_t mod);
int64_t is_order_15_i64_i64(int64_t g, int64_t p);
int64_t find_gen_i64_i64(int64_t p, int64_t d);
int32_t main(void);
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) {
r = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(r)) * ((__int128)(b)))), (((__int128)(mod))))));
}
b = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(b)) * ((__int128)(b)))), (((__int128)(mod))))));
e = FLOW_CHECKED_DIV((e), (2));
}
return r;
}
int64_t is_order_15_i64_i64(int64_t g, int64_t p) {
if (g == 1) {
return 0;
}
int64_t g2 = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(g)) * ((__int128)(g)))), (((__int128)(p))))));
int64_t g3 = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(g2)) * ((__int128)(g)))), (((__int128)(p))))));
if (g3 == 1) {
return 0;
}
int64_t g5 = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(g2)) * ((__int128)(g3)))), (((__int128)(p))))));
if (g5 == 1) {
return 0;
}
return 1;
}
int64_t find_gen_i64_i64(int64_t p, int64_t d) {
int64_t exp = FLOW_CHECKED_DIV(((p - 1)), (d));
int64_t* bases = (int64_t*)(calloc(30, 8));
int64_t nb = 25;
bases[0] = 2;
bases[1] = 3;
bases[2] = 5;
bases[3] = 7;
bases[4] = 11;
bases[5] = 13;
bases[6] = 17;
bases[7] = 19;
bases[8] = 23;
bases[9] = 29;
bases[10] = 31;
bases[11] = 37;
bases[12] = 41;
bases[13] = 43;
bases[14] = 47;
bases[15] = 53;
bases[16] = 59;
bases[17] = 61;
bases[18] = 67;
bases[19] = 71;
bases[20] = 73;
bases[21] = 79;
bases[22] = 83;
bases[23] = 89;
bases[24] = 97;
int64_t i = 0;
while (i < nb) {
int64_t a = bases[i];
if (a >= p) {
break;
}
int64_t g = modpow_i64_i64_i64(a, exp, p);
if ((d == 3 || d == 5)) {
if (g != 1) {
free(bases);
return g;
}
} else {
if (is_order_15_i64_i64(g, p) == 1) {
free(bases);
return g;
}
}
i = (i + 1);
}
int64_t a2 = 2;
while ((a2 < p && a2 < 500)) {
int64_t g2 = modpow_i64_i64_i64(a2, exp, p);
if ((d == 3 || d == 5)) {
if (g2 != 1) {
free(bases);
return g2;
}
} else {
if (is_order_15_i64_i64(g2, p) == 1) {
free(bases);
return g2;
}
}
a2 = (a2 + 1);
}
free(bases);
return 1;
}
int32_t main(void) {
int64_t L = 100000000000;
int64_t M = 100000000;
int64_t size = (FLOW_CHECKED_DIV((M), (2)) + 1);
int8_t* odd = (int8_t*)(calloc(size, 1));
if (odd == NULL) {
return 1;
}
int64_t i = 0;
while (i < size) {
odd[i] = 1;
i = (i + 1);
}
odd[0] = 0;
int64_t p = 3;
while ((p * p) <= M) {
if (odd[FLOW_CHECKED_SHR((p), (1))] != 0) {
int64_t cur = FLOW_CHECKED_SHR(((p * p)), (1));
while (cur < size) {
odd[cur] = 0;
cur = (cur + p);
}
}
p = (p + 2);
}
int32_t* d_table = (int32_t*)(calloc(30, 4));
i = 0;
while (i < 30) {
d_table[i] = 1;
i = (i + 1);
}
d_table[1] = 15;
d_table[11] = 5;
d_table[7] = 3;
d_table[13] = 3;
d_table[19] = 3;
int64_t ans = (2 * FLOW_CHECKED_DIV(((L + 1)), (2)));
p = 3;
while (p <= M) {
if (odd[FLOW_CHECKED_SHR((p), (1))] != 0) {
int64_t d = ((int64_t)(d_table[FLOW_CHECKED_MOD((p), (30))]));
int64_t q = FLOW_CHECKED_DIV((L), (p));
int64_t t = FLOW_CHECKED_MOD((L), (p));
if (d == 1) {
int64_t cnt = q;
if (t == (p - 1)) {
cnt = (cnt + 1);
}
ans = (ans + (p * cnt));
} else {
int64_t g = find_gen_i64_i64(p, d);
int64_t threshold = (p - t);
int64_t u = 1;
int64_t extra = 0;
int64_t k = 0;
while (k < d) {
if (u >= threshold) {
extra = (extra + 1);
}
u = ((int64_t)(FLOW_CHECKED_MOD(((((__int128)(u)) * ((__int128)(g)))), (((__int128)(p))))));
k = (k + 1);
}
ans = (ans + (p * ((d * q) + extra)));
}
}
p = (p + 2);
}
printf("%lld\n", ans);
free(d_table);
free(odd);
return 0;
}