Problem 293

Sum of distinct pseudo-Fortunate numbers for admissible N < 10^9.

Answer2209
Output2209
StatusPASS
Native helperno
Runtime50 ms
Peak memory1360 KB
Time complexityO(n^2) (estimated)
Space complexityO(n^2) (estimated)

Performance comparison

MetricOur solutionBest known
Time complexityO(n^2)O(n log log n)
Space complexityO(n^2)O(n)
ApproachFlow solutionSieve-based search
VerdictSuboptimal

Flow source

# Project Euler 293
# Sum of distinct pseudo-Fortunate numbers for admissible N < 10^9.

extern {
    function calloc(n: i64, size: i64) -> ptr<void>
    function free(p: ptr<void>) -> void
}

function is_prime_mr(n: i64) -> bool {
    if n < 2 { return false }
    if n < 4 { return true }
    if n % 2 == 0 || n % 3 == 0 { return false }
    let mut i: i64 = 5
    while i * i <= n {
        if n % i == 0 || n % (i + 2) == 0 { return false }
        i = i + 6
    }
    return true
}

function main() -> i32 {
    let limit: i64 = 1000000000
    let factors: ptr<i64> = calloc(9, 8)
    factors[0] = 2; factors[1] = 3; factors[2] = 5; factors[3] = 7
    factors[4] = 11; factors[5] = 13; factors[6] = 17; factors[7] = 19; factors[8] = 23

    # generate admissible via stack
    let MAXA: i64 = 10000
    let adm: ptr<i64> = calloc(MAXA, 8)
    let todo_n: ptr<i64> = calloc(MAXA, 8)
    let todo_m: ptr<i64> = calloc(MAXA, 8)
    if adm == null || todo_n == null || todo_m == null { return 1 }
    let mut ac: i64 = 0
    let mut tc: i64 = 1
    todo_n[0] = 2
    todo_m[0] = 0

    while tc > 0 {
        # pop smallest (linear scan since few)
        let mut best: i64 = 0
        for bi in 1..tc {
            if todo_n[bi] < todo_n[best] { best = bi }
        }
        let number: i64 = todo_n[best]
        let maxp: i64 = todo_m[best]
        todo_n[best] = todo_n[tc - 1]
        todo_m[best] = todo_m[tc - 1]
        tc = tc - 1
        adm[ac] = number
        ac = ac + 1
        let mut i: i64 = 0
        while i <= maxp + 1 {
            if i >= 9 { break }
            let next: i64 = number * factors[i]
            if next < limit {
                let nm: i64 = maxp
                if i > nm { nm = i }
                # push if not already present
                let mut found: bool = false
                let mut j: i64 = 0
                while j < tc {
                    if todo_n[j] == next {
                        if todo_m[j] < nm { todo_m[j] = nm }
                        found = true
                        break
                    }
                    j = j + 1
                }
                if !found {
                    todo_n[tc] = next
                    todo_m[tc] = nm
                    tc = tc + 1
                }
            }
            i = i + 1
        }
    }

    # collect distinct M
    let seen: ptr<i8> = calloc(10000, 1)
    if seen == null { return 1 }
    let mut sum: i64 = 0
    for ai in 0..ac {
        let n: i64 = adm[ai]
        let mut m: i64 = 3
        while true {
            if is_prime_mr(n + m) {
                if seen[m] == 0 {
                    seen[m] = 1
                    sum = sum + m
                }
                break
            }
            m = m + 2
        }
    }
    printf("%lld\n", sum)
    free(seen); free(adm); free(todo_n); free(todo_m); free(factors)
    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; }

bool is_prime_mr_i64(int64_t n);
int32_t main(void);



bool is_prime_mr_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;
}

int32_t main(void) {
    int64_t limit = 1000000000;
    int64_t* factors = (int64_t*)(calloc(9, 8));
    factors[0] = 2;
    factors[1] = 3;
    factors[2] = 5;
    factors[3] = 7;
    factors[4] = 11;
    factors[5] = 13;
    factors[6] = 17;
    factors[7] = 19;
    factors[8] = 23;
    int64_t MAXA = 10000;
    int64_t* adm = (int64_t*)(calloc(MAXA, 8));
    int64_t* todo_n = (int64_t*)(calloc(MAXA, 8));
    int64_t* todo_m = (int64_t*)(calloc(MAXA, 8));
    if (((adm == NULL || todo_n == NULL) || todo_m == NULL)) {
        return 1;
    }
    int64_t ac = 0;
    int64_t tc = 1;
    todo_n[0] = 2;
    todo_m[0] = 0;
    while (tc > 0) {
        int64_t best = 0;
        int32_t __flow_step_1 = 1;
        for (int32_t bi = 1; (1 <= tc) ? bi < tc : bi > tc; bi += (1 <= tc) ? 1 : -1) {
            if (todo_n[bi] < todo_n[best]) {
                best = bi;
            }
        }
        int64_t number = todo_n[best];
        int64_t maxp = todo_m[best];
        todo_n[best] = todo_n[(tc - 1)];
        todo_m[best] = todo_m[(tc - 1)];
        tc = (tc - 1);
        adm[ac] = number;
        ac = (ac + 1);
        int64_t i = 0;
        while (i <= (maxp + 1)) {
            if (i >= 9) {
                break;
            }
            int64_t next = (number * factors[i]);
            if (next < limit) {
                int64_t nm = maxp;
                if (i > nm) {
                    nm = i;
                }
                bool found = 0;
                int64_t j = 0;
                while (j < tc) {
                    if (todo_n[j] == next) {
                        if (todo_m[j] < nm) {
                            todo_m[j] = nm;
                        }
                        found = 1;
                        break;
                    }
                    j = (j + 1);
                }
                if ((!(found))) {
                    todo_n[tc] = next;
                    todo_m[tc] = nm;
                    tc = (tc + 1);
                }
            }
            i = (i + 1);
        }
    }
    int8_t* seen = (int8_t*)(calloc(10000, 1));
    if (seen == NULL) {
        return 1;
    }
    int64_t sum = 0;
    int32_t __flow_step_2 = 1;
    for (int32_t ai = 0; (0 <= ac) ? ai < ac : ai > ac; ai += (0 <= ac) ? 1 : -1) {
        int64_t n = adm[ai];
        int64_t m = 3;
        while (1) {
            if (is_prime_mr_i64((n + m))) {
                if (seen[m] == 0) {
                    seen[m] = 1;
                    sum = (sum + m);
                }
                break;
            }
            m = (m + 2);
        }
    }
    printf("%lld\n", sum);
    free(seen);
    free(adm);
    free(todo_n);
    free(todo_m);
    free(factors);
    return 0;
}

Generated MLIR

module {
  llvm.func @printf(!llvm.ptr, ...) -> i32
  llvm.mlir.global internal constant @str_0("%lld\n\00") {addr_space = 0 : i32} : !llvm.array<6 x i8>
  func.func private @calloc(i64, i64) -> !llvm.ptr
  func.func private @free(!llvm.ptr) -> ()
  func.func @is_prime_mr(%arg0: i64) -> i1 {
    %0 = arith.constant 2 : i32
    %2 = arith.extsi %0 : i32 to i64
    %1 = arith.cmpi slt, %arg0, %2 : i64
    cf.cond_br %1, ^bb0, ^bb1
    ^bb0:
      %3 = arith.constant 0 : i1
      func.return %3 : i1
    ^bb1:
      cf.br ^bb2
    ^bb2:
    %4 = arith.constant 4 : i32
    %6 = arith.extsi %4 : i32 to i64
    %5 = arith.cmpi slt, %arg0, %6 : i64
    cf.cond_br %5, ^bb3, ^bb4
    ^bb3:
      %7 = arith.constant 1 : i1
      func.return %7 : i1
    ^bb4:
      cf.br ^bb5
    ^bb5:
    %8 = arith.constant 2 : i32
    %10 = arith.extsi %8 : i32 to i64
    %9 = arith.remsi %arg0, %10 : i64
    %11 = arith.constant 0 : i32
    %13 = arith.extsi %11 : i32 to i64
    %12 = arith.cmpi eq, %9, %13 : i64
    %14 = scf.if %12 -> (i1) {
      %15 = arith.constant true
      scf.yield %15 : i1
    } else {
      %16 = arith.constant 3 : i32
      %18 = arith.extsi %16 : i32 to i64
      %17 = arith.remsi %arg0, %18 : i64
      %19 = arith.constant 0 : i32
      %21 = arith.extsi %19 : i32 to i64
      %20 = arith.cmpi eq, %17, %21 : i64
      scf.yield %20 : i1
    }
    cf.cond_br %14, ^bb6, ^bb7
    ^bb6:
      %22 = arith.constant 0 : i1
      func.return %22 : i1
    ^bb7:
      cf.br ^bb8
    ^bb8:
    %23 = arith.constant 5 : i32
    %24 = arith.extsi %23 : i32 to i64
    %25 = llvm.mlir.constant(1 : i64) : i64
    %26 = llvm.alloca %25 x i64 : (i64) -> !llvm.ptr
    llvm.store %24, %26 : i64, !llvm.ptr
    cf.br ^bb9
    ^bb9:
    %27 = llvm.load %26 : !llvm.ptr -> i64
    %28 = llvm.load %26 : !llvm.ptr -> i64
    %29 = arith.muli %27, %28 : i64
    %30 = arith.cmpi sle, %29, %arg0 : i64
    cf.cond_br %30, ^bb10, ^bb11
    ^bb10:
      %31 = llvm.load %26 : !llvm.ptr -> i64
      %32 = arith.remsi %arg0, %31 : i64
      %33 = arith.constant 0 : i32
      %35 = arith.extsi %33 : i32 to i64
      %34 = arith.cmpi eq, %32, %35 : i64
      %36 = scf.if %34 -> (i1) {
        %37 = arith.constant true
        scf.yield %37 : i1
      } else {
        %38 = llvm.load %26 : !llvm.ptr -> i64
        %39 = arith.constant 2 : i32
        %41 = arith.extsi %39 : i32 to i64
        %40 = arith.addi %38, %41 : i64
        %42 = arith.remsi %arg0, %40 : i64
        %43 = arith.constant 0 : i32
        %45 = arith.extsi %43 : i32 to i64
        %44 = arith.cmpi eq, %42, %45 : i64
        scf.yield %44 : i1
      }
      cf.cond_br %36, ^bb12, ^bb13
      ^bb12:
        %46 = arith.constant 0 : i1
        func.return %46 : i1
      ^bb13:
        cf.br ^bb14
      ^bb14:
      %47 = llvm.load %26 : !llvm.ptr -> i64
      %48 = arith.constant 6 : i32
      %50 = arith.extsi %48 : i32 to i64
      %49 = arith.addi %47, %50 : i64
      llvm.store %49, %26 : i64, !llvm.ptr
      cf.br ^bb9
    ^bb11:
    %51 = arith.constant 1 : i1
    func.return %51 : i1
  }
  func.func @main() -> i32 {
    %52 = arith.constant 1000000000 : i32
    %53 = arith.extsi %52 : i32 to i64
    %55 = arith.constant 9 : i32
    %56 = arith.constant 8 : i32
    %57 = arith.extsi %55 : i32 to i64
    %58 = arith.extsi %56 : i32 to i64
    %54 = func.call @calloc(%57, %58) : (i64, i64) -> !llvm.ptr
    %59 = arith.constant 2 : i32
    %60 = arith.constant 0 : i32
    %61 = arith.extsi %59 : i32 to i64
    %62 = arith.extsi %60 : i32 to i64
    %63 = llvm.getelementptr %54[%62] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %61, %63 : i64, !llvm.ptr
    %64 = arith.constant 3 : i32
    %65 = arith.constant 1 : i32
    %66 = arith.extsi %64 : i32 to i64
    %67 = arith.extsi %65 : i32 to i64
    %68 = llvm.getelementptr %54[%67] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %66, %68 : i64, !llvm.ptr
    %69 = arith.constant 5 : i32
    %70 = arith.constant 2 : i32
    %71 = arith.extsi %69 : i32 to i64
    %72 = arith.extsi %70 : i32 to i64
    %73 = llvm.getelementptr %54[%72] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %71, %73 : i64, !llvm.ptr
    %74 = arith.constant 7 : i32
    %75 = arith.constant 3 : i32
    %76 = arith.extsi %74 : i32 to i64
    %77 = arith.extsi %75 : i32 to i64
    %78 = llvm.getelementptr %54[%77] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %76, %78 : i64, !llvm.ptr
    %79 = arith.constant 11 : i32
    %80 = arith.constant 4 : i32
    %81 = arith.extsi %79 : i32 to i64
    %82 = arith.extsi %80 : i32 to i64
    %83 = llvm.getelementptr %54[%82] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %81, %83 : i64, !llvm.ptr
    %84 = arith.constant 13 : i32
    %85 = arith.constant 5 : i32
    %86 = arith.extsi %84 : i32 to i64
    %87 = arith.extsi %85 : i32 to i64
    %88 = llvm.getelementptr %54[%87] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %86, %88 : i64, !llvm.ptr
    %89 = arith.constant 17 : i32
    %90 = arith.constant 6 : i32
    %91 = arith.extsi %89 : i32 to i64
    %92 = arith.extsi %90 : i32 to i64
    %93 = llvm.getelementptr %54[%92] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %91, %93 : i64, !llvm.ptr
    %94 = arith.constant 19 : i32
    %95 = arith.constant 7 : i32
    %96 = arith.extsi %94 : i32 to i64
    %97 = arith.extsi %95 : i32 to i64
    %98 = llvm.getelementptr %54[%97] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %96, %98 : i64, !llvm.ptr
    %99 = arith.constant 23 : i32
    %100 = arith.constant 8 : i32
    %101 = arith.extsi %99 : i32 to i64
    %102 = arith.extsi %100 : i32 to i64
    %103 = llvm.getelementptr %54[%102] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %101, %103 : i64, !llvm.ptr
    %104 = arith.constant 10000 : i32
    %105 = arith.extsi %104 : i32 to i64
    %107 = arith.constant 8 : i32
    %108 = arith.extsi %107 : i32 to i64
    %106 = func.call @calloc(%105, %108) : (i64, i64) -> !llvm.ptr
    %110 = arith.constant 8 : i32
    %111 = arith.extsi %110 : i32 to i64
    %109 = func.call @calloc(%105, %111) : (i64, i64) -> !llvm.ptr
    %113 = arith.constant 8 : i32
    %114 = arith.extsi %113 : i32 to i64
    %112 = func.call @calloc(%105, %114) : (i64, i64) -> !llvm.ptr
    %115 = llvm.mlir.zero : !llvm.ptr
    %116 = llvm.icmp "eq" %106, %115 : !llvm.ptr
    %117 = scf.if %116 -> (i1) {
      %118 = arith.constant true
      scf.yield %118 : i1
    } else {
      %119 = llvm.mlir.zero : !llvm.ptr
      %120 = llvm.icmp "eq" %109, %119 : !llvm.ptr
      scf.yield %120 : i1
    }
    %121 = scf.if %117 -> (i1) {
      %122 = arith.constant true
      scf.yield %122 : i1
    } else {
      %123 = llvm.mlir.zero : !llvm.ptr
      %124 = llvm.icmp "eq" %112, %123 : !llvm.ptr
      scf.yield %124 : i1
    }
    cf.cond_br %121, ^bb15, ^bb16
    ^bb15:
      %125 = arith.constant 1 : i32
      func.return %125 : i32
    ^bb16:
      cf.br ^bb17
    ^bb17:
    %126 = arith.constant 0 : i32
    %127 = arith.extsi %126 : i32 to i64
    %128 = llvm.mlir.constant(1 : i64) : i64
    %129 = llvm.alloca %128 x i64 : (i64) -> !llvm.ptr
    llvm.store %127, %129 : i64, !llvm.ptr
    %130 = arith.constant 1 : i32
    %131 = arith.extsi %130 : i32 to i64
    %132 = llvm.mlir.constant(1 : i64) : i64
    %133 = llvm.alloca %132 x i64 : (i64) -> !llvm.ptr
    llvm.store %131, %133 : i64, !llvm.ptr
    %134 = arith.constant 2 : i32
    %135 = arith.constant 0 : i32
    %136 = arith.extsi %134 : i32 to i64
    %137 = arith.extsi %135 : i32 to i64
    %138 = llvm.getelementptr %109[%137] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %136, %138 : i64, !llvm.ptr
    %139 = arith.constant 0 : i32
    %140 = arith.constant 0 : i32
    %141 = arith.extsi %139 : i32 to i64
    %142 = arith.extsi %140 : i32 to i64
    %143 = llvm.getelementptr %112[%142] : (!llvm.ptr, i64) -> !llvm.ptr, i64
    llvm.store %141, %143 : i64, !llvm.ptr
    cf.br ^bb18
    ^bb18:
    %144 = llvm.load %133 : !llvm.ptr -> i64
    %145 = arith.constant 0 : i32
    %147 = arith.extsi %145 : i32 to i64
    %146 = arith.cmpi sgt, %144, %147 : i64
    cf.cond_br %146, ^bb19, ^bb20
    ^bb19:
      %148 = arith.constant 0 : i32
      %149 = arith.extsi %148 : i32 to i64
      %150 = llvm.mlir.constant(1 : i64) : i64
      %151 = llvm.alloca %150 x i64 : (i64) -> !llvm.ptr
      llvm.store %149, %151 : i64, !llvm.ptr
      %152 = arith.constant 1 : i32
      %153 = llvm.load %133 : !llvm.ptr -> i64
      %154 = arith.index_cast %152 : i32 to index
      %155 = arith.index_cast %153 : i32 to index
      %157 = arith.constant 1 : index
      %158 = arith.constant -1 : index
      %159 = arith.cmpi sle, %154, %155 : index
      %156 = arith.select %159, %157, %158 : index
      cf.br ^bb21(%154 : index)
      ^bb21(%160: index):
      %161 = arith.cmpi slt, %160, %155 : index
      %162 = arith.cmpi sgt, %160, %155 : index
      %163 = arith.select %159, %161, %162 : i1
      cf.cond_br %163, ^bb22(%160 : index), ^bb23(%160 : index)
      ^bb22(%164: index):
        %166 = arith.index_cast %164 : index to i64
        %167 = llvm.getelementptr %109[%166] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        %165 = llvm.load %167 : !llvm.ptr -> i64
        %169 = llvm.load %151 : !llvm.ptr -> i64
        %170 = llvm.getelementptr %109[%169] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        %168 = llvm.load %170 : !llvm.ptr -> i64
        %171 = arith.cmpi slt, %165, %168 : i64
        cf.cond_br %171, ^bb24, ^bb25
        ^bb24:
          %172 = arith.index_cast %164 : index to i64
          llvm.store %172, %151 : i64, !llvm.ptr
          cf.br ^bb26
        ^bb25:
          cf.br ^bb26
        ^bb26:
        %173 = arith.addi %164, %156 : index
        cf.br ^bb21(%173 : index)
      ^bb23(%174: index):
      %176 = llvm.load %151 : !llvm.ptr -> i64
      %177 = llvm.getelementptr %109[%176] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %175 = llvm.load %177 : !llvm.ptr -> i64
      %179 = llvm.load %151 : !llvm.ptr -> i64
      %180 = llvm.getelementptr %112[%179] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %178 = llvm.load %180 : !llvm.ptr -> i64
      %182 = llvm.load %133 : !llvm.ptr -> i64
      %183 = arith.constant 1 : i32
      %185 = arith.extsi %183 : i32 to i64
      %184 = arith.subi %182, %185 : i64
      %186 = llvm.getelementptr %109[%184] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %181 = llvm.load %186 : !llvm.ptr -> i64
      %187 = llvm.load %151 : !llvm.ptr -> i64
      %188 = llvm.getelementptr %109[%187] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      llvm.store %181, %188 : i64, !llvm.ptr
      %190 = llvm.load %133 : !llvm.ptr -> i64
      %191 = arith.constant 1 : i32
      %193 = arith.extsi %191 : i32 to i64
      %192 = arith.subi %190, %193 : i64
      %194 = llvm.getelementptr %112[%192] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %189 = llvm.load %194 : !llvm.ptr -> i64
      %195 = llvm.load %151 : !llvm.ptr -> i64
      %196 = llvm.getelementptr %112[%195] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      llvm.store %189, %196 : i64, !llvm.ptr
      %197 = llvm.load %133 : !llvm.ptr -> i64
      %198 = arith.constant 1 : i32
      %200 = arith.extsi %198 : i32 to i64
      %199 = arith.subi %197, %200 : i64
      llvm.store %199, %133 : i64, !llvm.ptr
      %201 = llvm.load %129 : !llvm.ptr -> i64
      %202 = llvm.getelementptr %106[%201] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      llvm.store %175, %202 : i64, !llvm.ptr
      %203 = llvm.load %129 : !llvm.ptr -> i64
      %204 = arith.constant 1 : i32
      %206 = arith.extsi %204 : i32 to i64
      %205 = arith.addi %203, %206 : i64
      llvm.store %205, %129 : i64, !llvm.ptr
      %207 = arith.constant 0 : i32
      %208 = arith.extsi %207 : i32 to i64
      %209 = llvm.mlir.constant(1 : i64) : i64
      %210 = llvm.alloca %209 x i64 : (i64) -> !llvm.ptr
      llvm.store %208, %210 : i64, !llvm.ptr
      cf.br ^bb27
      ^bb27:
      %211 = llvm.load %210 : !llvm.ptr -> i64
      %212 = arith.constant 1 : i32
      %214 = arith.extsi %212 : i32 to i64
      %213 = arith.addi %178, %214 : i64
      %215 = arith.cmpi sle, %211, %213 : i64
      cf.cond_br %215, ^bb28, ^bb29
      ^bb28:
        %216 = llvm.load %210 : !llvm.ptr -> i64
        %217 = arith.constant 9 : i32
        %219 = arith.extsi %217 : i32 to i64
        %218 = arith.cmpi sge, %216, %219 : i64
        cf.cond_br %218, ^bb30, ^bb31
        ^bb30:
          cf.br ^bb29
        ^bb31:
          cf.br ^bb32
        ^bb32:
        %221 = llvm.load %210 : !llvm.ptr -> i64
        %222 = llvm.getelementptr %54[%221] : (!llvm.ptr, i64) -> !llvm.ptr, i64
        %220 = llvm.load %222 : !llvm.ptr -> i64
        %223 = arith.muli %175, %220 : i64
        %224 = arith.cmpi slt, %223, %53 : i64
        cf.cond_br %224, ^bb33, ^bb34
        ^bb33:
          %225 = llvm.load %210 : !llvm.ptr -> i64
          %226 = arith.cmpi sgt, %225, %178 : i64
          %227 = scf.if %226 -> (i64) {
            %228 = llvm.load %210 : !llvm.ptr -> i64
            scf.yield %228 : i64
          } else {
            scf.yield %178 : i64
          }
          %229 = arith.constant 0 : i1
          %230 = llvm.mlir.constant(1 : i64) : i64
          %231 = llvm.alloca %230 x i1 : (i64) -> !llvm.ptr
          llvm.store %229, %231 : i1, !llvm.ptr
          %232 = arith.constant 0 : i32
          %233 = arith.extsi %232 : i32 to i64
          %234 = llvm.mlir.constant(1 : i64) : i64
          %235 = llvm.alloca %234 x i64 : (i64) -> !llvm.ptr
          llvm.store %233, %235 : i64, !llvm.ptr
          cf.br ^bb36
          ^bb36:
          %236 = llvm.load %235 : !llvm.ptr -> i64
          %237 = llvm.load %133 : !llvm.ptr -> i64
          %238 = arith.cmpi slt, %236, %237 : i64
          cf.cond_br %238, ^bb37, ^bb38
          ^bb37:
            %240 = llvm.load %235 : !llvm.ptr -> i64
            %241 = llvm.getelementptr %109[%240] : (!llvm.ptr, i64) -> !llvm.ptr, i64
            %239 = llvm.load %241 : !llvm.ptr -> i64
            %242 = arith.cmpi eq, %239, %223 : i64
            cf.cond_br %242, ^bb39, ^bb40
            ^bb39:
              %244 = llvm.load %235 : !llvm.ptr -> i64
              %245 = llvm.getelementptr %112[%244] : (!llvm.ptr, i64) -> !llvm.ptr, i64
              %243 = llvm.load %245 : !llvm.ptr -> i64
              %246 = arith.cmpi slt, %243, %227 : i64
              cf.cond_br %246, ^bb42, ^bb43
              ^bb42:
                %247 = llvm.load %235 : !llvm.ptr -> i64
                %248 = llvm.getelementptr %112[%247] : (!llvm.ptr, i64) -> !llvm.ptr, i64
                llvm.store %227, %248 : i64, !llvm.ptr
                cf.br ^bb44
              ^bb43:
                cf.br ^bb44
              ^bb44:
              %249 = arith.constant 1 : i1
              llvm.store %249, %231 : i1, !llvm.ptr
              cf.br ^bb38
            ^bb40:
              cf.br ^bb41
            ^bb41:
            %250 = llvm.load %235 : !llvm.ptr -> i64
            %251 = arith.constant 1 : i32
            %253 = arith.extsi %251 : i32 to i64
            %252 = arith.addi %250, %253 : i64
            llvm.store %252, %235 : i64, !llvm.ptr
            cf.br ^bb36
          ^bb38:
          %254 = llvm.load %231 : !llvm.ptr -> i1
          %256 = arith.constant 1 : i1
          %255 = arith.xori %254, %256 : i1
          cf.cond_br %255, ^bb45, ^bb46
          ^bb45:
            %258 = llvm.load %133 : !llvm.ptr -> i64
            %259 = llvm.getelementptr %109[%258] : (!llvm.ptr, i64) -> !llvm.ptr, i64
            llvm.store %223, %259 : i64, !llvm.ptr
            %260 = llvm.load %133 : !llvm.ptr -> i64
            %261 = llvm.getelementptr %112[%260] : (!llvm.ptr, i64) -> !llvm.ptr, i64
            llvm.store %227, %261 : i64, !llvm.ptr
            %262 = llvm.load %133 : !llvm.ptr -> i64
            %263 = arith.constant 1 : i32
            %265 = arith.extsi %263 : i32 to i64
            %264 = arith.addi %262, %265 : i64
            llvm.store %264, %133 : i64, !llvm.ptr
            cf.br ^bb47
          ^bb46:
            cf.br ^bb47
          ^bb47:
          cf.br ^bb35
        ^bb34:
          cf.br ^bb35
        ^bb35:
        %266 = llvm.load %210 : !llvm.ptr -> i64
        %267 = arith.constant 1 : i32
        %269 = arith.extsi %267 : i32 to i64
        %268 = arith.addi %266, %269 : i64
        llvm.store %268, %210 : i64, !llvm.ptr
        cf.br ^bb27
      ^bb29:
      cf.br ^bb18
    ^bb20:
    %271 = arith.constant 10000 : i32
    %272 = arith.constant 1 : i32
    %273 = arith.extsi %271 : i32 to i64
    %274 = arith.extsi %272 : i32 to i64
    %270 = func.call @calloc(%273, %274) : (i64, i64) -> !llvm.ptr
    %275 = llvm.mlir.zero : !llvm.ptr
    %276 = llvm.icmp "eq" %270, %275 : !llvm.ptr
    cf.cond_br %276, ^bb48, ^bb49
    ^bb48:
      %277 = arith.constant 1 : i32
      func.return %277 : i32
    ^bb49:
      cf.br ^bb50
    ^bb50:
    %278 = arith.constant 0 : i32
    %279 = arith.extsi %278 : i32 to i64
    %280 = llvm.mlir.constant(1 : i64) : i64
    %281 = llvm.alloca %280 x i64 : (i64) -> !llvm.ptr
    llvm.store %279, %281 : i64, !llvm.ptr
    %282 = arith.constant 0 : i32
    %283 = llvm.load %129 : !llvm.ptr -> i64
    %284 = arith.index_cast %282 : i32 to index
    %285 = arith.index_cast %283 : i32 to index
    %287 = arith.constant 1 : index
    %288 = arith.constant -1 : index
    %289 = arith.cmpi sle, %284, %285 : index
    %286 = arith.select %289, %287, %288 : index
    cf.br ^bb51(%284 : index)
    ^bb51(%290: index):
    %291 = arith.cmpi slt, %290, %285 : index
    %292 = arith.cmpi sgt, %290, %285 : index
    %293 = arith.select %289, %291, %292 : i1
    cf.cond_br %293, ^bb52(%290 : index), ^bb53(%290 : index)
    ^bb52(%294: index):
      %296 = arith.index_cast %294 : index to i64
      %297 = llvm.getelementptr %106[%296] : (!llvm.ptr, i64) -> !llvm.ptr, i64
      %295 = llvm.load %297 : !llvm.ptr -> i64
      %298 = arith.constant 3 : i32
      %299 = arith.extsi %298 : i32 to i64
      %300 = llvm.mlir.constant(1 : i64) : i64
      %301 = llvm.alloca %300 x i64 : (i64) -> !llvm.ptr
      llvm.store %299, %301 : i64, !llvm.ptr
      cf.br ^bb54
      ^bb54:
      %302 = arith.constant 1 : i1
      cf.cond_br %302, ^bb55, ^bb56
      ^bb55:
        %304 = llvm.load %301 : !llvm.ptr -> i64
        %305 = arith.addi %295, %304 : i64
        %303 = func.call @is_prime_mr(%305) : (i64) -> i1
        cf.cond_br %303, ^bb57, ^bb58
        ^bb57:
          %307 = llvm.load %301 : !llvm.ptr -> i64
          %308 = llvm.getelementptr %270[%307] : (!llvm.ptr, i64) -> !llvm.ptr, i8
          %306 = llvm.load %308 : !llvm.ptr -> i8
          %309 = arith.constant 0 : i32
          %311 = arith.extsi %306 : i8 to i32
          %310 = arith.cmpi eq, %311, %309 : i32
          cf.cond_br %310, ^bb60, ^bb61
          ^bb60:
            %312 = arith.constant 1 : i32
            %313 = llvm.load %301 : !llvm.ptr -> i64
            %314 = arith.trunci %312 : i32 to i8
            %315 = llvm.getelementptr %270[%313] : (!llvm.ptr, i64) -> !llvm.ptr, i8
            llvm.store %314, %315 : i8, !llvm.ptr
            %316 = llvm.load %281 : !llvm.ptr -> i64
            %317 = llvm.load %301 : !llvm.ptr -> i64
            %318 = arith.addi %316, %317 : i64
            llvm.store %318, %281 : i64, !llvm.ptr
            cf.br ^bb62
          ^bb61:
            cf.br ^bb62
          ^bb62:
          cf.br ^bb56
        ^bb58:
          cf.br ^bb59
        ^bb59:
        %319 = llvm.load %301 : !llvm.ptr -> i64
        %320 = arith.constant 2 : i32
        %322 = arith.extsi %320 : i32 to i64
        %321 = arith.addi %319, %322 : i64
        llvm.store %321, %301 : i64, !llvm.ptr
        cf.br ^bb54
      ^bb56:
      %323 = arith.addi %294, %286 : index
      cf.br ^bb51(%323 : index)
    ^bb53(%324: index):
    %325 = llvm.mlir.addressof @str_0 : !llvm.ptr
    %326 = llvm.load %281 : !llvm.ptr -> i64
    %327 = llvm.call @printf(%325, %326) vararg(!llvm.func<i32 (ptr, ...)>) : (!llvm.ptr, i64) -> i32
    func.call @free(%270) : (!llvm.ptr) -> ()
    func.call @free(%106) : (!llvm.ptr) -> ()
    func.call @free(%109) : (!llvm.ptr) -> ()
    func.call @free(%112) : (!llvm.ptr) -> ()
    func.call @free(%54) : (!llvm.ptr) -> ()
    %333 = arith.constant 0 : i32
    func.return %333 : i32
  }
}