First learned such a fast method to determine prime numbers
This is the Fermat test; as long as it is determined that these three bases {2,7,61} are all true
It can correctly determine that numbers below 2^32 are prime
The complexity is O(logN)
//
// GGGGGGGGGGGGG CCCCCCCCCCCCC AAA
// GGG::::::::::::G CCC::::::::::::C A:::A
// GG:::::::::::::::G CC:::::::::::::::C A:::::A
// G:::::GGGGGGGG::::G C:::::CCCCCCCC::::C A:::::::A
// G:::::G GGGGGG C:::::C CCCCCC A:::::::::A
//G:::::G C:::::C A:::::A:::::A
//G:::::G C:::::C A:::::A A:::::A
//G:::::G GGGGGGGGGGC:::::C A:::::A A:::::A
//G:::::G G::::::::GC:::::C A:::::A A:::::A
//G:::::G GGGGG::::GC:::::C A:::::AAAAAAAAA:::::A
//G:::::G G::::GC:::::C A:::::::::::::::::::::A
// G:::::G G::::G C:::::C CCCCCC A:::::AAAAAAAAAAAAA:::::A
// G:::::GGGGGGGG::::G C:::::CCCCCCCC::::C A:::::A A:::::A
// GG:::::::::::::::G CC:::::::::::::::C A:::::A A:::::A
// GGG::::::GGG:::G CCC::::::::::::C A:::::A A:::::A
// GGGGGG GGGG CCCCCCCCCCCCCAAAAAAA AAAAAAA
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <climits>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <cctype>
#include <utility>
#include <ctime>
using namespace std;
#ifdef DEBUG
#define VAR(a,b) decltype(b) a=(b)
#define debug(...) printf("DEBUG: "),printf(__VA_ARGS__)
#define gettime() end_time=clock();printf("now running time is %.7f\\n",(float)(end_time - start_time)/CLOCKS_PER_SEC);
#else
#define VAR(a,b) __typeof(b) a=(b)
#define debug(...)
#define gettime()
#endif
typedef unsigned int uint;
typedef unsigned long long int Int;
#define Set(a,s) memset(a,s,sizeof(a))
#define Write(w) freopen(w,"w",stdout)
#define Read(r) freopen(r,"r",stdin)
#define Pln() printf("\\n")
#define I_de(x,n)for(int i=0;i<n;i++)printf("%d ",x[i]);Pln()
#define De(x)printf(#x"%d\\n",x)
#define For(i,x)for(int i=0;i<x;i++)
#define CON(x,y) x##y
#define Pmz(dp,nx,ny)for(int hty=0;hty<ny;hty++){for(int htx=0;htx<nx;htx++){\\
printf("%d ",dp[htx][hty]);}Pln();}
#define M 55
#define PII pair<int,int>
#define PB push_back
#define oo INT_MAX
#define Set_oo 0x3f
#define FOR(a,b) for(VAR(a,(b).begin());a!=(b).end();++a)
#define eps 1e-6
clock_t start_time=clock(), end_time;
bool xdy(double x,double y){return x>y+eps;}
bool xddy(double x,double y){return x>y-eps;}
bool xcy(double x,double y){return x<y-eps;}
bool xcdy(double x,double y){return x<y+eps;}
int min3(int x,int y,int z){
int tmp=min(x,y);
return min(tmp,z);
}
int max3(int x,int y,int z){
int tmp=max(x,y);
return max(tmp,z);
}
Int powmod(Int b,Int u,Int n){
Int ans=1;
Int base=b;
while(u){
if(u&1)
ans=ans*base%n;
base=base*base%n;
u>>=1;
}
return ans;
}
bool suspect(Int b,Int n){
Int exp=0;
Int t=n-1;
while(!(t&1)){
exp++;
t>>=1;
}
Int xi=powmod(b,t,n);
if(xi==1||xi==n-1)return true;
for(int i=0;i<exp-1;i++){
xi=xi*xi%n;
if(xi==1)return false;
if(xi==n-1)return true;
}
return false;
}
Int b,mx,mn;
int main() {
ios_base::sync_with_stdio(0);
// putchar(suspect(3,121)?'y':'n');
int ff=0;
while(~scanf("%llu%llu%llu",&b,&mn,&mx)&&b+mn+mx){
Int omn=mn,omx=mx;
vector<Int> ans;
int op=0;
if(!(mn&1))mn++;
if(!(mx&1))mx--;
for(Int i=mn;i<=mx;i+=2){
// printf("%lld\\n",i);
bool isp=false;
if(suspect(2,i)&&suspect(7,i)&&suspect(61,i)){
isp=true;
}else{
op++;
}
if((i&1)&&suspect(b,i)==true&&isp==false){
ans.PB(i);
}
}
int size=ans.size();
if(ff++)Pln();
printf("There are %d odd non-prime numbers between %llu and %llu.\\n",op,omn,omx);
if(size){
printf("%d suspects fail in base %llu:\\n",size,b);
FOR(it,ans){
printf("%lld\\n",*it);
}
}else printf("There are no failures in base %llu.\\n",b);
}
}