(cache)minimal-elements-of-the-prime-numbers/code/k2GMP.cc at main · xayahrainie4793/minimal-elements-of-the-prime-numbers · GitHub

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#include <list>
#include <cmath>
#include <string>
#include <random>
#include <algorithm>
#include <vector>
#include <iostream>
#include <fstream>
#include <time.h>
#include <stdlib.h>
#include <gmpxx.h>
#include <gmp.h>
#define cyclemax 12
#define nbfact 2 // number of simultaneous prime factors considered for a family
#define mxfact 2 // largest simultaneous factor
#define maxrem 100 // largest number of remainders
using namespace std;

// code base mxlg [d1[@d2] [d3[@d4]]]
// tries to extend the current kernel for base with primes up to length mxlg
// if d1 is specified, we only consider families starting with digit d1 (up to d2 if specified)
// if d3 is specified, we only consider families ending with digit d3 (up to d4 if specified)
// new found primes are gathered in a file newprimes{base}-suffix
// and families to be still analyzed are gathered in a file left{base}-suffix
// details of the exploration are send to the standard output

char tr[128]; int w[128];
struct simfact { int vct[nbfact]; };
simfact zrem,vrem;
vector <simfact> simrem;
using family=vector <string>;
using sint=long unsigned int; // std::vector<std::__cxx11::basic_string<char> >::size_type;
vector <string> found;
ifstream kern; ofstream result,reject,court;
sint b;
vector <sint> fact; string covering;
clock_t cpustarttime,cputime;
mpz_class nt,nprime,nlong,n1,y,z,z1,z2,bx,zz1,zz2,zzz;
sint k,lgmax,nbsmall;
mpz_t rtt,rt1,rt2;
random_device rd;
mt19937 gen(rd()); // set random gen

string s10(mpz_class x)
{mpz_class y=x; int r; string s="";
 while (y!=0){r=mpz_class{y%10}.get_si();y=y/10;s=tr[r]+s;}
 return s;
}

string sb(mpz_class x)
{mpz_class y=x; int r; string s="";if(x==0)return "0";
 while (y!=0){r=mpz_class{y%b}.get_si();y=y/b;s=tr[r]+s;}
 return s;
}

string familystrip(family f)
 {string ss; sint i;
  ss="";
  for(i=0;i<f.size();i=i+2)ss=ss+f[i];
  return(ss);
 }

string stringf(family f)
 {sint i; string s;if(f.size()==1)return f[0];
  if(f.size()==1){s=f[0];return s;}
  for(i=0;i<f.size()-2;i=i+2)s=s+f[i]+"{"+f[i+1]+"}";
  s=s+f[i];
  return s;
 }

long long gcd(long long i,long long j)
 {long long ii,jj,kk; if(i==0)return j;if(j==0)return i;
  if(j>i){ii=j;jj=i;} else {ii=i;jj=j;}
 while(jj!=0){kk=ii%jj;ii=jj;jj=kk;}
  return ii;}

mpz_class gcd(mpz_class i,mpz_class j)
 {mpz_class ii,jj,kk; if(i==0)return j;if(j==0)return i;
  if(j>i){ii=j;jj=i;} else {ii=i;jj=j;}
 while(jj!=0){kk=ii%jj;ii=jj;jj=kk;}
  return ii;}

 int min( int i,  int j)
 {if(i<=j)return i;else return j;}

void buildfact()
 {sint kk,n; bool ok;
  fact.push_back(2);fact.push_back(3);fact.push_back(5);
  for(n=7;n<b*b*b;n++)
   {ok=true;for(kk=0;fact[kk]*fact[kk]<=n;kk++)
             if(n%fact[kk]==0){ok=false;break;}
    if(ok){fact.push_back(n);}
   }
  for(nbsmall=0;fact[nbsmall]<b*b;nbsmall++)continue;
 }

bool cover(string  el)
// checks if some member of found is a substring of el
 {sint i,j,it;
  for(it=0;it!=found.size();it++)
     {if(el==found[it]){covering=found[it];return true;}
      if(el.length()<found[it].length())continue;
      i=0;j=0;
      while(i<el.length())
       {if(el[i]==(found[it])[j])
        {i++;j++;if(j>=(found[it]).length()){covering=found[it];return true;}
         if(i>=el.length())break;
        }
        else {i++;if(i>=el.length())break;}
       }
     }
  return false;
 }

bool newprime(string s)
 {sint i; mpz_class n1=0;
  for(i=0;i<s.length();i++)n1=n1*b+w[s[i]];
  if(mpz_probab_prime_p(n1.get_mpz_t(),50)>0)
    {nprime++;court<<s<<"\n";found.push_back(s);court.flush();return true;}
  else {return false;}
 }

bool difsq(string s1,int y,string s2)
 {sint i; mpz_class bb,bx,xb,yb,zy,gg,xx,yy,zz,z1,z2; bool test;
  xb=0;yb=0;bx=1;bb=b;zy=y;
  if(!mpz_root(rtt,bb.get_mpz_t(),2))return false;
  for(i=0;i<s1.size();i++)xb=xb*b+w[s1[i]];
  for(i=0;i<s2.size();i++)yb=yb*b+w[s2[i]];
  for(i=0;i<s2.size();i++)bx=bx*b;
  gg=gcd(zy,bb-1);
  xx=(y+(b-1)*xb)/gg;
  if(!mpz_root(rtt,xx.get_mpz_t(),2))return false;
  yy=(bx*y-(b-1)*yb)/gg;
  if(!mpz_root(rtt,yy.get_mpz_t(),2))return false;
  z2=mpz_class(rtt);
  zz=bx*xx;
  mpz_root(rtt,zz.get_mpz_t(),2);
  z1=mpz_class(rtt);
  test=(z1-z2)>((b-1)/gg);
  if(test)
    {cout<<s1<<"{"<<tr[y]<<"}"<<s2<<" is a difference of squares "
         <<b<<", "<<xx<<" and "<<yy<<"\n"; return true;}
  return false;
 }

bool p4p4p4b(string s1,int y,string s2)
// checks if we have a factorisation of x^4+4.y^4 for {d}
 {sint i; mpz_class bb,bx,xb,yb,zy,gg,xx,yy,zz,z1,z2; bool t1,t2;
  xb=0;yb=0;bx=1;bb=b;zy=y;
  if(!mpz_root(rtt,bb.get_mpz_t(),4))return false;
  for(i=0;i<s1.size();i++)xb=xb*b+w[s1[i]];
  for(i=0;i<s2.size();i++)yb=yb*b+w[s2[i]];
  for(i=0;i<s2.size();i++)bx=bx*b;
  gg=gcd(zy,bb-1);
  xx=(y+(b-1)*xb)/gg;
  yy=((b-1)*yb-bx*y)/gg;if(yy<=0)return false;
  if(xx%4==0){z1=xx/4; t1=mpz_root(rt1,z1.get_mpz_t(),4);
              t2=mpz_root(rt2,yy.get_mpz_t(),4);
              if(t1&&t2)
                {cout<<s1<<"{"<<sb(y)<<"}"<<s2<<" has a Germain's factorisation ("
                     <<z1<<","<<yy<<")\n";return true;}
             }
  if(yy%4==0){z2=yy/4; t1=mpz_root(rt2,z2.get_mpz_t(),4);
              t2=mpz_root(rt2,xx.get_mpz_t(),4);
              if(t1&&t2)
                {cout<<s1<<"{"<<sb(y)<<"}"<<s2<<" has a Germain's factorisation ("
                     <<xx<<","<<z2<<")\n";return true;}
             }
  return false;
 }

bool p4p4p4bb(string s1,string sddk,string s2)
// checks if we have a factorisation of x^4+4.y^4 for {dd} or {dddd}
 {sint i,k; mpz_class  bb,bx,xb,yb,y,gg,xx,yy,zz,z1,z2; bool t1,t2;

  xb=0;yb=0;bx=1;y=0;k=sddk.size();for(i=0;i<k;i++)y=y*b+w[sddk[i]];
  bb=b;if(k==2)if(!mpz_root(rtt,bb.get_mpz_t(),2))return false;
  if(s2.size()%k!=0)
   {for(i=0;i<s2.size()%k;i++){s2=sddk[0]+s2;
                               if(cover(s1+s2))return false;
                               if(newprime(s1+s2))return false;}
    for(i=i;i<k;i++){s1=s1+sddk[0];
                       if(cover(s1+s2))return false;
                       if(newprime(s1+s2))return false;}
   }
  for(i=0;i<s1.size();i++)xb=xb*b+w[s1[i]];
  for(i=0;i<s2.size();i++)yb=yb*b+w[s2[i]];
  for(i=0;i<s2.size();i++)bx=bx*b;
  gg=gcd(y,bx-1);
  xx=(y+(bx-1)*xb)/gg;
  yy=((bx-1)*yb-bx*y)/gg;if(yy<=0)return false;
  if(xx%4==0){z1=xx/4; t1=mpz_root(rt1,z1.get_mpz_t(),4);
              t2=mpz_root(rt2,yy.get_mpz_t(),4);
              if(t1&&t2)
                {cout<<s1<<"{"<<sb(y)<<"}"<<s2<<" has a Germain's factorisation ("
                     <<z1<<","<<yy<<")\n";return true;}
             }
  if(yy%4==0){z2=yy/4; t1=mpz_root(rt2,z2.get_mpz_t(),4);
              t2=mpz_root(rt2,xx.get_mpz_t(),4);
              if(t1&&t2)
                {cout<<s1<<"{"<<sb(y)<<"}"<<s2<<" has a Germain's factorisation ("
                     <<xx<<","<<z2<<")\n";return true;}
             }
  return false;
 }

bool difpowb(string s1,int y,string s2,int k)
 {sint i; mpz_class bb,bx,xb,yb,zy,gg,xx,yy,zz,rt,rtk,z1,z2; bool test;
  xb=0;yb=0;bx=1;bb=b;zy=y;
  if(!mpz_root(rtt,bb.get_mpz_t(),k))return false;
  for(i=0;i<s1.size();i++)xb=xb*b+w[s1[i]];
  for(i=0;i<s2.size();i++)yb=yb*b+w[s2[i]];
  for(i=0;i<s2.size();i++)bx=bx*b;
  gg=gcd(zy,bb-1);
  xx=(y+(b-1)*xb)/gg;
  if(!mpz_root(rtt,xx.get_mpz_t(),k))return false;
  yy=(bx*y-(b-1)*yb)/gg;
  if(yy<0&&k%2==0)return false;
  if(!mpz_root(rtt,yy.get_mpz_t(),k))return false;
  zz=bx*xx;
  mpz_root(rt1,zz.get_mpz_t(),k);z1=mpz_class(rt1);
  mpz_root(rt2,yy.get_mpz_t(),k);z2=mpz_class(rt2);
  test=(z1-z2)>((b-1)/gg);
  if(test)
    {cout<<s1<<"{"<<sb(y)<<"}"<<s2<<" is a difference of "
         <<k<<"th powers: "<<b<<"^*."<<xx<<" and "<<yy<<"\n";
     return true;}
  return false;
 }

bool difpowbb(string s1,string sddk,string s2)
 {sint i,k; mpz_class bb,bx,xb,yb,y,gg,xx,yy,zz,rt,rtk,z1,z2; bool test;
  xb=0;yb=0;bx=1;y=0;k=sddk.size();for(i=0;i<k;i++)y=y*b+w[sddk[i]];
  bb=1;for(i=0;i<k;i++){bb=bb*b;}
  if(s2.size()%k!=0)
   {for(i=0;i<s2.size()%k;i++){s2=sddk[0]+s2;
                               if(cover(s1+s2))return false;
                               if(newprime(s1+s2))return false;}
    for(i=i;i<k;i++){s1=s1+sddk[0];
                       if(cover(s1+s2))return false;
                       if(newprime(s1+s2))return false;}
   }
  for(i=0;i<s1.size();i++)xb=xb*b+w[s1[i]];
  for(i=0;i<s2.size();i++)yb=yb*b+w[s2[i]];
  for(i=0;i<s2.size();i++)bx=bx*b;
  gg=gcd(y,bb-1);
  xx=(y+(bb-1)*xb)/gg;
  if(!mpz_root(rtt,xx.get_mpz_t(),k)){return false;}
  yy=(bx*y-(bb-1)*yb)/gg;
  if(yy<0&&k%2==0)return false;
  if(!mpz_root(rtt,yy.get_mpz_t(),k))return false;
  zz=bx*xx;
  mpz_root(rt1,zz.get_mpz_t(),k);z1=mpz_class(rt1);
  mpz_root(rt2,yy.get_mpz_t(),k);z2=mpz_class(rt2);
  test=(z1-z2)>((bb-1)/gg);
  if(test)
    {cout<<s1<<"{"<<sb(y)<<"}"<<s2<<" is a difference of "
         <<k<<"th powers: "<<bb<<", "<<xx<<" and "<<yy<<"\n";
     return true;}
  return false;
 }

bool smallfactor(family f)
 {sint i,ii,i1,i2;mpz_class n1,z1,z2,bx,zz1,zz2,zzz;
  for(ii=0;ii<nbsmall;ii++)
      {i=fact[ii];n1=0;
       for(i1=0;i1<f.size();i1++)
        {if(i1%2==0)
          {for(i2=0;i2<f[i1].size();i2++)n1=(n1*b+w[f[i1][i2]])%i;
          }
          else
          {for(i2=0;i2<f[i1].size();i2++){if(n1!=((n1*b+w[f[i1][i2]])%i))break;}
           if(i2!=f[i1].size())break;
          }
        }
                 ") and ("<<ic2<<","<<f[ic2][jc2]<<")\n";
           handelf(ff);
          } else
          {ff[ic1]=ff[ic1]+p2;ff.insert(ff.begin()+ic1+1,p1);ff.insert(ff.begin()+ic1+2,fff[ic1]+p1);
           ff.insert(ff.begin()+ic2+3,p2);ff.insert(ff.begin()+ic2+4,f[ic2]);
           cout<<"extend212 "<<stringf(f)<<" with ("<<ic1<<","<<f[ic1][jc1]<<
                 ") and ("<<ic2<<","<<f[ic2][jc2]<<")\n";
           handelf(ff);ff=fff;
           ff[ic1]=ff[ic1]+p1;ff.insert(ff.begin()+ic1+1,p2);ff.insert(ff.begin()+ic1+2,fff[ic2]+p2);
           ff.insert(ff.begin()+ic2+3,p1);ff.insert(ff.begin()+ic2+4,f[ic1]);
           cout<<"extend221 "<<stringf(f)<<" with ("<<ic1<<","<<f[ic1][jc2]<<
                 ") and ("<<ic2<<","<<f[ic2][jc1]<<")\n";
           handelf(ff);
          }
   }

} // fin du traitement de la base

int main(int argc, char *argv[])
{string ms,pref,prefms,p,ss,chunkl,chunkr; family f;
 sint i,ilb,ilh,irb,irh,il,ir,j;
 mpz_init(rtt); mpz_init(rt1); mpz_init(rt2);
 ms=argv[1];b=atoi(argv[1]); lgmax=atoi(argv[2]);
 pref="kernel"; prefms=pref+ms;
 kern.open(prefms.c_str());
 if(argc>3){chunkl=argv[3];ms=ms+'-'+argv[3];}else{chunkl="";}
 if(argc>4){chunkr=argv[4];ms=ms+'-'+argv[4];}else{chunkr="";}
 pref="result"; prefms=pref+ms;
 result.open(prefms.c_str(),ios::out);
 pref="newprimes"; prefms=pref+ms;
 court.open(prefms.c_str(),ios::out);
 pref="left"; prefms=pref+ms;
 reject.open(prefms.c_str(),ios::out);
 for(char c='0';c<='9';c++){w[c]=0+c-'0';tr[0+c-'0']=c;}
 for(char c='A';c<='Z';c++){w[c]=10+c-'A';tr[10+c-'A']=c;}
 for(char c='a';c<='z';c++){w[c]=36+c-'a';tr[36+c-'a']=c;}
 buildfact();
 if(chunkl!="")cout<<" for initial digits "<<chunkl;
 if(chunkr!="")cout<<" and for terminal digits "<<chunkr;
 cout<<"\n";
 cout<<"lgmax="<<lgmax<<"\n";cout.flush();
 found.clear();nt=0;nprime=0;nlong=0;
 for(int i=0;i<nbfact;i++)zrem.vct[i]=0;
 while(kern>>p)
      {found.push_back(p);
      }
// initialisation
 if(chunkl==""){ilb=1;ilh=b-1;}
    else {for(i=0;i<chunkl.length();i++)if(chunkl[i]=='@')break;
          if(i==chunkl.length()){ilb=stoi(chunkl);ilh=ilb;}
            else {ilb=stoi(chunkl.substr(0,i));ilh=stoi(chunkl.substr(i+1));}
         }
 if(chunkr==""){irb=1;irh=b-1;}
    else {for(i=0;i<chunkr.length();i++)if(chunkr[i]=='@')break;
          if(i==chunkr.length()){irb=stoi(chunkr);irh=irb;}
            else {irb=stoi(chunkr.substr(0,i));irh=stoi(chunkr.substr(i+1));}
         }
 cpustarttime=clock();
 ss="";for(j=0;j<b;j++)ss=ss+tr[j];
 f.clear();f.push_back("0");f.push_back(ss);f.push_back("0");
 for(il=ilb;il<=ilh;il++)for(ir=irb;ir<=irh;ir++)if(gcd(b,ir)==1)
     {f[0][0]=tr[il];f[2][0]=tr[ir];
//construction of the familles to be explored from the first and last digits
      handelf(f);
     }

 cputime = clock()-cpustarttime; cputime=cputime/1000000;
 result<<"\nFinally, in "<<cputime<<" time units, we explored "
       <<nt<<" families of numbers for base "<<b;
 if(chunkl!="")result<<" and the initial digit "<<chunkl;
 if(chunkr!="")result<<" and the terminal digit "<<chunkr;
 result<<"\nthere remains "<<nprime<<" primes to incorporate in the kernel, and "
       <<nlong<<" families to analyse\n";
} // end main