Recent content by Yorshick

Proof of criteria of twin primes is contained in attached file. It follows from primality criteria (section 4).

n=122. N1=S1(122)=6*122+5=737; N2=S2(122)=6*122+7=739 122=6*x*y-x+y-1; y= (123+x)/(6*x+1); x=1; y=124/7; x=2;y=125/13; x=3;y=126/19; x=4; y=127/25; x=5;y=128/31... x=11; y=134/67 = 2 - integer solution N1=737 and N2=739 are not twin primes

Example. n=37. N1=S1(37)=37*6+5=227; N2=S2(37)=37*6+7=229 37=6*x*y-x+y-1; y=(38+x)/(6*x+1); x=1; y=39/7; x=2;y=40/13; x=3;y=41/19;...no integer solution 37=6*x*y-x-y-1; y=(38+x)/(6*x-1); x=1; y=39/5; x=2;y=40/11; x=3;y=41/17;...no integer solution 37=6*x*y+x+y-1...

Yes, this criteria of twin primes based on derived "alternative definition" of prime numbers: Natural numbers that do not appear in arrays P1(i,j)=6*i*j-i+j-1; i=1,2,3,...; j>=i P2(i,j)=6*i*j+i-j-1; i=1,2,3,...; j>=i+1 are indexes p of ALL PRIMES in the sequence S1(p)=6*p+5, p=0,1,2,3...

I propose the following criteria of twin primes conjecture: Natural numbers N1=6n+5 and N2=6n+7, n=0,1,2,3,.. are twins if and only if no one of three equations n=6xy-x+y-1; x>=1; y>=1 n=6xy-x-y-1; x>=1; y>=x; n=6xy+x+y-1; x>=1; y>=x; has integer solution. Attached: convenient C++ program for...

I can propose the following criteria of twin primes conjecture: Natural numbers N1=6n+5 and N2=6n+7, n=0,1,2,3,.. are twins if and only if no one of three equations n=6xy-x+y-1; x>=1; y>=1 n=6xy-x-y-1; x>=1; y>=x; n=6xy+x+y-1; x>=1; y>=x; has integer solution. Attached: convenient C++...