This was really helpful, however there’s one thing I did not get. How did you come up with this polynomial when you said: “The “clever” way is to write the polynomial in the form {T_2(x) = c(x-(\pi/2))^2 + b(x – (\pi/2)) + a”.

]]>let S the count of the digit of a number. EX S(99)=S(18)=S(9)=9.

S(i) must be between [2;9], i>1.

to verify if two number’s are not twin:

“IF S(p)*S(p+2) different to 8 then p and p+2 are not twin prime numbers”

note that

1)S(p+i)=S(S(p)+i)

2)S(i)*S(j)=S(i*j)

EX:

S(111413131313131343534231331663534342442442442355343434351141)=7 and S(111413131313131343534231331663534342442442442355343434351143)=7+2

S(7*9)=S(63)=S(9)=9 . this two numbers are not twin prime numbers (vérified by hand on less then 3 minutes). ]]>