## 10394 - Twin Primes

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The problem is that the contents of your array table is undefined. You could initialize it with either:
[c]memset(table, 1, 18409201);[/c]
or by just looping over all elements and setting them to some nonzero value. Otherwise it seems to work fine. I notice that you call the isPrime in the sieve loop, why not look it up in table instead? It would save you some time when running the program.

Best regards
hager
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Location: Ume

Thank you!!

That was the problem, I got AC now!
Max108
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### 10394

I think my source makes output in time, but I got TLE. ㅜ_ㅜ

plz check this.
[cpp]#include <iostream>
#include <cmath>

using namespace std;

int prime1[10000];
bool prime2[20000000];

void main(void)
{
int c1, c2;
int input=0;
bool p;

for(c1=2; c1<=4473; c1++)
{
p=true;
for(c2=2; c2<sqrt(c1); c2++)
{
if(c1%c2==0)
{
p=false;
break;
}
}
if(p)
{
prime1[input++]=c1;
}
}
for(c1=0; c1<20000000; c1++)
{
prime2[c1]=true;
}
for(c1=0; c1<input; c1++)
{
for(c2=2; c2<=10000000; c2++)
{
if(c2*prime1[c1]>=20000000) break;
prime2[c2*prime1[c1]]=false;
}
}
int t1=0;
while(1)
{
cin >> input;
t1++;
if(cin.eof()) break;
if(input<0) break;
c2=0;
for(c1=2; c1<20000000; c1++)
{
if(prime2[c1+2] && prime2[c1])
{
c2++;
}
if(c2==input)
{
cout << "(" << c1 << ", " << c1+2 << ")" << endl;
break;
}
}
if(t1==10000) break;
}
}[/cpp]
Park, Kwang-Kyu
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Jalal wrote:Thanx Michniewski!
u r right.........
eric!
try with the following one

for(m= 6 ; m < x; m+=6)
if(prime(m-1) && prime(m+1))
printf("%ld %ld\n", m-1, m+1);

the algorithm is great.
but..how do u guys discover that all twins prime are subset of (6*k-1,6*k+1), for k is integers?

however, i am still TLE using this algorithm, why?
[cpp]
#include <iostream>
using namespace std;
int i,j,k,n;
int prime[100005];
int counter;
int isprime(int);
void main(void)
{
prime[1]=3;
prime[2]=5;

counter=3;
for (i=12;counter<=100002;i+=6)
{
if (isprime(i-1) && isprime(i+1))
{
prime[counter++]=i-1;
}

}
while (1)
{
cin>>n;
if (cin.eof())
break;
cout<<"("<<prime[n]<<", "<<prime[n]+2<<")"<<endl;
}
}

int isprime(int get)
{
int k;
for (k=3;k*k<=get;k+=2)
{
if (get % k ==0)
return 0;
}
return 1;
}
[/cpp]
SilVer DirectXer
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Use sieve for your prime checker..
Larry
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Location: Hong Kong and New York City

Larry wrote:Use sieve for your prime checker..

thanks....
but, could you explain more details?
how to use a sieve for the prime checker?
SilVer DirectXer
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Posts: 39
Joined: Wed Jan 22, 2003 11:02 am

### HOW DO IT FASTER?

[pascal]
program acm10394; {Twince Prime Numbers}
{type integer = longint;}
const maxn = 4500;
koltw = 100000;
var ck : array[1 .. maxn] of boolean;
list : array[1 .. 700] of integer;
tw : array[1 .. koltw] of integer;
n, l : integer;

procedure get_primes; {Eratosphen}
var i, j: integer;
begin
fillchar(ck, sizeof(ck), true);
for i := 3 to 67 do
if ck[i] then begin
j := i * i;
while j <= maxn do begin
ck[j] := false;
j := j + i;
end;
end;

list[1]:=2; l:=1;
i:=1;
while i<=maxn do begin
inc(i, 2);
if ck[i] then begin
inc(l);
list[l] := i;
end;
end; {number of prime numbers - l}
end;

function be_prime( x : integer) : boolean; {prime or not}
var i,j : integer;
begin
j := trunc(sqrt(x));
be_prime := false;
i:=2;
while list[i] <= j do begin
if x mod list[i] = 0 then exit;
inc(i);
end;
be_prime := true;
end;

procedure twins;
var i, k: integer;
begin
tw[1]:=3; i:=1; k:=0;
while i<koltw do begin
inc(k, 6);
if be_prime(k-1) then
if be_prime(k+1) then begin
inc(i);
tw[i]:=k-1;
end;
end;
end;

begin
{ assign(input, 'input.txt');
reset(input);}
get_primes;
twins;
while not eof do begin
writeln('(', tw[n], ', ', tw[n]+2, ')');
end;
end.
[/pascal][/pascal]
pavelph
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Location: Russia, Saint-Petersburg

SilVer DirectXer:
but..how do u guys discover that all twins prime are subset of (6*k-1,6*k+1), for k is integers?

Let q and q + 2 be twin primes. The number between them is (clearly) q + 1.
Aside from 2, every prime number is odd. So q and q + 2 must both be odd, as both are prime. Hence, q + 1 is even. i.e. q + 1 is divisible by 2.
For any three consecutive integers, exactly one of them is divisible by 3. So either q = 3 and q + 2 = 5 [as 3 | q, q prime => q = 3] or q + 1 is divisible by 3. [And 3 | q + 2 is extraneous since, as before, it would require q + 2 = 3 => q = 1, which isn't prime].
Hence, the twin primes are (3, 5) or (q, q + 2) where q + 1 is divisible by 2 * 3 = 6. The result now follows.

As for the sieve method for generating primes, see an article about Eratosthenes' Sieve, e.g. http://mathworld.wolfram.com/EratosthenesSieve.html

pavelph:
I'm sorry, but I don't know Pascal very well. But, I think that calling be_prime() in twins() is the cause of the slowness since you'll end up calling it so many times.
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Location: United States

I am getting RTE in my program. Please help me to find my bug. Here is my code:
[c]#include <stdio.h>
#include <math.h>

const int max = 20000000;
char p[2500100];

#define isprime(n) (p[n/8] & (1<<(7-n % 8 )))

void seive()
{
int i,j;

for(i=3; i<=max; i+=2)
p[i/8] = p[i/8]|(1<<7-i % 8 );

int lim = sqrt(max);

for(i=3; i<=lim; i+=2)
if((p[i/8] & (1<<(7-i % 8 ))))
for(j=i; i*j<=max; j+=2)
p[i*j/8] = p[i*j/8] & ~(1<<7-(i*j) % 8 );
}

void main()
{
seive();
long s[100100];
long i, j;

for(i=3, j=1; j<100010; i+=2)
if(isprime(i) && isprime(i+2))
s[j++] = i;

while(1==scanf("%ld", &i))
printf("(%ld, %ld)\n", s[i], s[i]+2);
}
[/c]
Subeen
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Joined: Tue Nov 06, 2001 2:00 am

### 10394

This problem seemed to me easy. But very often a simple looking problem makes us crazy by fooling. I have received Run Time Error but don't know why. Please help me.

Here's my code:

..........deleted later
Last edited by Ferdous on Sun Mar 07, 2004 12:11 pm, edited 1 time in total.
I am destined to live on this cruel world........
Ferdous
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Posts: 26
Joined: Sun Dec 14, 2003 1:17 pm

### right

Hi Ferdous,

Try to make the twin and prime array global.

that is;

[c]
char prime[MAX+1];
long twin[100005];

int main()
{

}
[/c]

Declaring huge arrays in the main function is the cause of RTE.

Hope it helps.

sohel
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Joined: Thu Jan 30, 2003 5:50 am
Location: University of Texas at San Antonio

[cpp]
#define MAX 20000000

int main(void)
{
char prime[MAX+1];
[/cpp]

You are trying to declare a very large array inside the main function, which causes overflow and hence the run time error.

Just declare large arrays as global.

shamim
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Joined: Mon Dec 30, 2002 10:10 am
Location: Dhaka

Thanks a lot for your help. I declared those two large arrays as global variables according to your suggession and got AC. But I can't understand why do the program crash if I declare so large array in the main function? Would you please explain it?
I am destined to live on this cruel world........
Ferdous
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Posts: 26
Joined: Sun Dec 14, 2003 1:17 pm

As far I know, the main function is a procedure which has a limited amount of data area.

So if you declare a large array inside main, it tries to use the limited data area of main, which of course is smaller than the array size, hence the program crashes.

But if you declare it global, it is located in a seperate memory area, which can handle such big array.

shamim
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Location: Dhaka

Thanks a lot , Shamim vai. You are a great helper !!
I am destined to live on this cruel world........
Ferdous
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