# Project Euler 233
# Sum of N <= 10^11 with f(N)=420 lattice points on circle.
import euler.nt { isqrt }
extern {
function calloc(n: i64, size: i64) -> ptr<void>
function free(p: ptr<void>) -> void
}
function iroot(n: i64, k: i32) -> i64 {
if n <= 1 || k == 1 { return n }
let mut x: i64 = 1
# rough init via sqrt repeatedly
if k == 3 {
x = (n |> isqrt |> isqrt) + 2
} elif k == 7 {
x = (n |> isqrt |> isqrt |> isqrt) + 2
} else {
x = isqrt(n)
}
while true {
let mut p: i64 = 1
let mut i: i32 = 0
let mut overflow: bool = false
while i < k {
if p > n / x { overflow = true; break }
p = p * x
i = i + 1
}
if !overflow && p <= n {
let mut p2: i64 = 1
let mut ok: bool = true
i = 0
while i < k {
if p2 > n / (x + 1) { ok = false; break }
p2 = p2 * (x + 1)
i = i + 1
}
if ok && p2 <= n {
x = x + 1
continue
}
return x
}
x = x - 1
if x <= 0 { return 0 }
}
return x
}
function bisect_right(a: ptr<i64>, n: i64, v: i64) -> i64 {
let mut lo: i64 = 0
let mut hi: i64 = n
while lo < hi {
let mid: i64 = (lo + hi) / 2
if a[mid] <= v { lo = mid + 1 }
else { hi = mid }
}
return lo
}
function main() -> i32 {
let LIMIT: i64 = 100000000000
let max_prime: i64 = LIMIT / (125 * 169)
let sieve: ptr<i8> = calloc(max_prime + 1, 1)
if sieve == null { return 1 }
let mut i: i64 = 0
while i <= max_prime {
sieve[i] = 1
i = i + 1
}
sieve[0] = 0; sieve[1] = 0
i = 2
while i * i <= max_prime {
if sieve[i] == 1 {
let mut j: i64 = i * i
while j <= max_prime {
sieve[j] = 0
j = j + i
}
}
i = i + 1
}
let primes1: ptr<i64> = calloc(max_prime / 5, 8)
let mut np: i64 = 0
i = 5
while i <= max_prime {
if sieve[i] == 1 && (i & 3) == 1 {
primes1[np] = i
np = np + 1
}
i = i + 2
}
let gmax: i64 = LIMIT / (125 * 169 * 17)
let allowed: ptr<i8> = calloc(gmax + 1, 1)
let prefix: ptr<i64> = calloc(gmax + 1, 8)
if allowed == null || prefix == null { return 1 }
i = 0
while i <= gmax {
allowed[i] = 1
i = i + 1
}
allowed[0] = 0
i = 0
while i < np {
let p: i64 = primes1[i]
if p > gmax { break }
let mut j: i64 = p
while j <= gmax {
allowed[j] = 0
j = j + p
}
i = i + 1
}
let mut s: i64 = 0
i = 1
while i <= gmax {
if allowed[i] == 1 { s = s + i }
prefix[i] = s
i = i + 1
}
let mut total: i64 = 0
# Pattern (10,2): 5^10 * q^2
let p10: i64 = 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5
if p10 <= LIMIT {
let qmax: i64 = isqrt(LIMIT / p10)
let iq: i64 = bisect_right(primes1, np, qmax)
let mut j: i64 = 0
while j < iq {
let q: i64 = primes1[j]
if q != 5 {
let base: i64 = p10 * q * q
let m: i64 = LIMIT / base
if m > gmax { m = gmax }
total = total + base * prefix[m]
}
j = j + 1
}
}
# Pattern (7,3)
let amax: i64 = iroot(LIMIT, 7)
let ia: i64 = bisect_right(primes1, np, amax)
let mut ii: i64 = 0
while ii < ia {
let a: i64 = primes1[ii]
let mut a7: i64 = 1
let mut t: i32 = 0
while t < 7 {
a7 = a7 * a
t = t + 1
}
if a7 > LIMIT { break }
let bmax: i64 = iroot(LIMIT / a7, 3)
let ib: i64 = bisect_right(primes1, np, bmax)
let mut j: i64 = 0
while j < ib {
let b: i64 = primes1[j]
if b != a {
let base: i64 = a7 * b * b * b
if base <= LIMIT {
let m: i64 = LIMIT / base
if m > gmax { m = gmax }
total = total + base * prefix[m]
}
}
j = j + 1
}
ii = ii + 1
}
# Pattern (3,2,1)
let p3max: i64 = iroot(LIMIT, 3)
let ip3: i64 = bisect_right(primes1, np, p3max)
ii = 0
while ii < ip3 {
let p3: i64 = primes1[ii]
let p3_3: i64 = p3 * p3 * p3
if p3_3 > LIMIT { break }
let q2max: i64 = isqrt(LIMIT / p3_3)
let iq: i64 = bisect_right(primes1, np, q2max)
let mut j: i64 = 0
while j < iq {
let q: i64 = primes1[j]
if q != p3 {
let base_pq: i64 = p3_3 * q * q
if base_pq <= LIMIT {
let rmax: i64 = LIMIT / base_pq
let ir: i64 = bisect_right(primes1, np, rmax)
let mut kk: i64 = 0
while kk < ir {
let r: i64 = primes1[kk]
if r != p3 && r != q {
let base: i64 = base_pq * r
let m: i64 = LIMIT / base
if m > gmax { m = gmax }
total = total + base * prefix[m]
}
kk = kk + 1
}
}
}
j = j + 1
}
ii = ii + 1
}
printf("%lld\n", total)
free(sieve); free(primes1); free(allowed); free(prefix)
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 iroot_i64_i32(int64_t n, int32_t k);
int64_t bisect_right_ptr_i64_i64_i64(int64_t* a, int64_t n, int64_t v);
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 iroot_i64_i32(int64_t n, int32_t k) {
if ((n <= 1 || k == 1)) {
return n;
}
int64_t x = 1;
if (k == 3) {
x = (isqrt_i64(isqrt_i64(n)) + 2);
} else if (k == 7) {
x = (isqrt_i64(isqrt_i64(isqrt_i64(n))) + 2);
} else {
x = isqrt_i64(n);
}
while (1) {
int64_t p = 1;
int32_t i = 0;
bool overflow = 0;
while (i < k) {
if (p > FLOW_CHECKED_DIV((n), (x))) {
overflow = 1;
break;
}
p = (p * x);
i = (i + 1);
}
if (((!(overflow)) && p <= n)) {
int64_t p2 = 1;
bool ok = 1;
i = 0;
while (i < k) {
if (p2 > FLOW_CHECKED_DIV((n), ((x + 1)))) {
ok = 0;
break;
}
p2 = (p2 * (x + 1));
i = (i + 1);
}
if ((ok && p2 <= n)) {
x = (x + 1);
continue;
}
return x;
}
x = (x - 1);
if (x <= 0) {
return 0;
}
}
return x;
}
int64_t bisect_right_ptr_i64_i64_i64(int64_t* a, int64_t n, int64_t v) {
int64_t lo = 0;
int64_t hi = n;
while (lo < hi) {
int64_t mid = FLOW_CHECKED_DIV(((lo + hi)), (2));
if (a[mid] <= v) {
lo = (mid + 1);
} else {
hi = mid;
}
}
return lo;
}
int32_t main(void) {
int64_t LIMIT = 100000000000;
int64_t max_prime = FLOW_CHECKED_DIV((LIMIT), ((125 * 169)));
int8_t* sieve = (int8_t*)(calloc((max_prime + 1), 1));
if (sieve == NULL) {
return 1;
}
int64_t i = 0;
while (i <= max_prime) {
sieve[i] = 1;
i = (i + 1);
}
sieve[0] = 0;
sieve[1] = 0;
i = 2;
while ((i * i) <= max_prime) {
if (sieve[i] == 1) {
int64_t j = (i * i);
while (j <= max_prime) {
sieve[j] = 0;
j = (j + i);
}
}
i = (i + 1);
}
int64_t* primes1 = (int64_t*)(calloc(FLOW_CHECKED_DIV((max_prime), (5)), 8));
int64_t np = 0;
i = 5;
while (i <= max_prime) {
if ((sieve[i] == 1 && (i & 3) == 1)) {
primes1[np] = i;
np = (np + 1);
}
i = (i + 2);
}
int64_t gmax = FLOW_CHECKED_DIV((LIMIT), (((125 * 169) * 17)));
int8_t* allowed = (int8_t*)(calloc((gmax + 1), 1));
int64_t* prefix = (int64_t*)(calloc((gmax + 1), 8));
if ((allowed == NULL || prefix == NULL)) {
return 1;
}
i = 0;
while (i <= gmax) {
allowed[i] = 1;
i = (i + 1);
}
allowed[0] = 0;
i = 0;
while (i < np) {
int64_t p = primes1[i];
if (p > gmax) {
break;
}
int64_t j = p;
while (j <= gmax) {
allowed[j] = 0;
j = (j + p);
}
i = (i + 1);
}
int64_t s = 0;
i = 1;
while (i <= gmax) {
if (allowed[i] == 1) {
s = (s + i);
}
prefix[i] = s;
i = (i + 1);
}
int64_t total = 0;
int64_t p10 = (((((((((5 * 5) * 5) * 5) * 5) * 5) * 5) * 5) * 5) * 5);
if (p10 <= LIMIT) {
int64_t qmax = isqrt_i64(FLOW_CHECKED_DIV((LIMIT), (p10)));
int64_t iq = bisect_right_ptr_i64_i64_i64(primes1, np, qmax);
int64_t j = 0;
while (j < iq) {
int64_t q = primes1[j];
if (q != 5) {
int64_t base = ((p10 * q) * q);
int64_t m = FLOW_CHECKED_DIV((LIMIT), (base));
if (m > gmax) {
m = gmax;
}
total = (total + (base * prefix[m]));
}
j = (j + 1);
}
}
int64_t amax = iroot_i64_i32(LIMIT, 7);
int64_t ia = bisect_right_ptr_i64_i64_i64(primes1, np, amax);
int64_t ii = 0;
while (ii < ia) {
int64_t a = primes1[ii];
int64_t a7 = 1;
int32_t t = 0;
while (t < 7) {
a7 = (a7 * a);
t = (t + 1);
}
if (a7 > LIMIT) {
break;
}
int64_t bmax = iroot_i64_i32(FLOW_CHECKED_DIV((LIMIT), (a7)), 3);
int64_t ib = bisect_right_ptr_i64_i64_i64(primes1, np, bmax);
int64_t j = 0;
while (j < ib) {
int64_t b = primes1[j];
if (b != a) {
int64_t base = (((a7 * b) * b) * b);
if (base <= LIMIT) {
int64_t m = FLOW_CHECKED_DIV((LIMIT), (base));
if (m > gmax) {
m = gmax;
}
total = (total + (base * prefix[m]));
}
}
j = (j + 1);
}
ii = (ii + 1);
}
int64_t p3max = iroot_i64_i32(LIMIT, 3);
int64_t ip3 = bisect_right_ptr_i64_i64_i64(primes1, np, p3max);
ii = 0;
while (ii < ip3) {
int64_t p3 = primes1[ii];
int64_t p3_3 = ((p3 * p3) * p3);
if (p3_3 > LIMIT) {
break;
}
int64_t q2max = isqrt_i64(FLOW_CHECKED_DIV((LIMIT), (p3_3)));
int64_t iq = bisect_right_ptr_i64_i64_i64(primes1, np, q2max);
int64_t j = 0;
while (j < iq) {
int64_t q = primes1[j];
if (q != p3) {
int64_t base_pq = ((p3_3 * q) * q);
if (base_pq <= LIMIT) {
int64_t rmax = FLOW_CHECKED_DIV((LIMIT), (base_pq));
int64_t ir = bisect_right_ptr_i64_i64_i64(primes1, np, rmax);
int64_t kk = 0;
while (kk < ir) {
int64_t r = primes1[kk];
if ((r != p3 && r != q)) {
int64_t base = (base_pq * r);
int64_t m = FLOW_CHECKED_DIV((LIMIT), (base));
if (m > gmax) {
m = gmax;
}
total = (total + (base * prefix[m]));
}
kk = (kk + 1);
}
}
}
j = (j + 1);
}
ii = (ii + 1);
}
printf("%lld\n", total);
free(sieve);
free(primes1);
free(allowed);
free(prefix);
return 0;
}