## 10394 - Twin Primes

Moderator: Board moderators

hager
New poster
Posts: 10
Joined: Wed Jan 01, 2003 4:26 am
Location: Ume
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
Max108
New poster
Posts: 5
Joined: Wed Jun 11, 2003 11:24 pm
Thank you!!

That was the problem, I got AC now! Park, Kwang-Kyu
New poster
Posts: 2
Joined: Tue Jul 15, 2003 2:49 pm

### 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;
bool prime2;

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]
SilVer DirectXer
New poster
Posts: 39
Joined: Wed Jan 22, 2003 11:02 am
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;
int counter;
int isprime(int);
void main(void)
{
prime=3;
prime=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]
Larry
Guru
Posts: 647
Joined: Wed Jun 26, 2002 10:12 pm
Location: Hong Kong and New York City
Contact:
Use sieve for your prime checker..
SilVer DirectXer
New poster
Posts: 39
Joined: Wed Jan 22, 2003 11:02 am
Larry wrote:Use sieve for your prime checker..
thanks....
but, could you explain more details?
how to use a sieve for the prime checker?
pavelph
Learning poster
Posts: 57
Joined: Wed Dec 10, 2003 7:32 pm
Location: Russia, Saint-Petersburg

### 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 then begin
j := i * i;
while j <= maxn do begin
ck[j] := false;
j := j + i;
end;
end;

list:=2; l:=1;
i:=1;
while i<=maxn do begin
inc(i, 2);
if ck 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 <= j do begin
if x mod list = 0 then exit;
inc(i);
end;
be_prime := true;
end;

procedure twins;
var i, k: integer;
begin
tw:=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:=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]
Learning poster
Posts: 73
Joined: Mon Oct 14, 2002 7:15 am
Location: United States
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.
Subeen
Experienced poster
Posts: 127
Joined: Tue Nov 06, 2001 2:00 am
Contact:
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;

#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;
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, s+2);
}
[/c]
Ferdous
New poster
Posts: 26
Joined: Sun Dec 14, 2003 1:17 pm
Contact:

### 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........
sohel
Guru
Posts: 856
Joined: Thu Jan 30, 2003 5:50 am
Location: New York

### right

Hi Ferdous,

Try to make the twin and prime array global.

that is;

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

int main()
{

}
[/c]

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

Hope it helps. shamim
A great helper
Posts: 498
Joined: Mon Dec 30, 2002 10:10 am
Location: Bozeman, Montana, USA
[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. Ferdous
New poster
Posts: 26
Joined: Sun Dec 14, 2003 1:17 pm
Contact:
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........
shamim
A great helper
Posts: 498
Joined: Mon Dec 30, 2002 10:10 am
Location: Bozeman, Montana, USA
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.
Ferdous
New poster
Posts: 26
Joined: Sun Dec 14, 2003 1:17 pm