Hi DR. Rohit, I am going to try to explain it to you , but every time I use enter code here I get a problem, but I will try to be brief and succinct.
1- I reached a formula which is z=(n-1)^2(n+1)^3 where n can be treated as prime number or a composite...I also use a second formula z2=(n-1)^2(n+5)^3..
2- If i get the result of the module for z ( Mod 3,5,7,11) for primes it gives me a list of numbers that are exclusive for prime and another list that are exclusive for composite odds...see the program 1 below:
3- I have evidences that it is possible to reach the position of a prime by looking at the result of ( prime/prime+1) and for the position ( position/position+1).
4-with that in mind i have the largest prime number 2^82589933-1, and if i add a number " h" to that number it will give me a new number...i want that new number to respect the modulus result given by the formula "z" Lets say {{2,0},{0,1}},{6,0}...that stands for the result of Mod5 and 7, Mod 3 and 3 z2, and Mod 11 and 11z2( for the second formula z2).
5-I want that number "h" to be added to the largest prime number to give me a result of the modulus for z and z2 with a certain value so that by choosing the number to be added I can select a number that by respecting the result of modulus gives me a high probability of it being a prime.
Here is the program I use to check if the result of the modulus of a certain huge number is prime or not, I use complement to select the exclusive pair of numbers that are of primes or of composites.
program 1
sq=Table[j,{j,100000}]
sq11=Table[j,{j,1000,2000}]
x=Select[sq,OddQ,(900)]
n1=Select[sq,CompositeQ,(400)]
n=Select[sq,PrimeQ,(400)]
z=(n-1)^2*(n+1)^3
g=Mod[z,3]
g2=Mod[z,5]
g3=Mod[z,7]
g4=Mod[z,11]
Select[n,PrimeQ,(200)]
Length[%]
z1=(n-1)^2*(n+5)^3
g1=Mod[z1,3]
g5=Mod[z1,11]
q=Riffle[g2,g3]
q1=Partition[q,2]
p=Riffle[g,g1]
q2=Partition[p,2]
r=Riffle[q1,q2]
h=Partition[r,2]
q3=Riffle[g4,g5]
q4=Partition[q3,2]
q5=Riffle[h,q4]
q55=List[q5]
q6=Partition[q5,2]
sq=Table[j,{j,100000}]
sq11=Table[j,{j,1000,2000}]
x=Select[sq,OddQ,(900)]
n=Select[sq,CompositeQ,(400)]
n1=Select[sq,PrimeQ,(400)]
z=(n-1)^2*(n+1)^3
g=Mod[z,3]
g2=Mod[z,5]
g3=Mod[z,7]
g4=Mod[z,11]
Select[n,PrimeQ,(200)]
Length[%]
z1=(n-1)^2*(n+5)^3
g1=Mod[z1,3]
g5=Mod[z1,11]
q=Riffle[g2,g3]
q1=Partition[q,2]
p=Riffle[g,g1]
q2=Partition[p,2]
r=Riffle[q1,q2]
h=Partition[r,2]
q3=Riffle[g4,g5]
q4=Partition[q3,2]
q5=Riffle[h,q4]
q55=List[q5]
q61=Partition[q5,2]
Complement[q61,q6]
Program 2 is the program to whcih i add a certain number "h" that will give me specific results for the next calculus of the Mod of z and z2 to that new number:
x=((1*10^24862047)-1)/(1*10^24862047)
y=(57*10^-24862049)
N[x,24862049]
N[y,24862051]
z=x+y
zz=N[z,24862051]
{x2}=x1/. NSolve[x1/(x1+1)==zz,{x1}]
{x4}=x3/. NSolve[((((2^82589933-1)*((x2*2)-1))+x3))/x3==(x2*2)+2,{x3}]
b=(2^82589933-1)+(((2^82589933-1)-x4)/2)
c=IntegerPart[b]
d=c+1
e=(2^82589933-1-d)/2
e1=IntegerPart[e]
f=2^82589933-1+e1-5
Table[Solve[((f-1+h)^2*(f+1+h)^3)==((f-1+h)^2*(f+1+h)^3*3)==((f-1+h)^2*(f+1+h)^3*5)==((f-1+h)^2*(f+1+h)^3*7)==0,Modulus->Prime[k]],{k,2,5}]
i=f+16
z1=(i-1)^2*(i+1)^3
g=Mod[z1,3]
g2=Mod[z1,5]
g3=Mod[z1,7]
g4=Mod[z1,11]
z12=(i-1)^2*(i+5)^3
g1=Mod[z12,3]
g5=Mod[z12,11]
