Mohsen Afshin
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 Apr 22 comment Last 2 digits of modular exponentiation @Mike,Yes, I want the last two digits of the first modular operation so it requires another (mod 100) on the result of the first mod. Apr 3 comment Numerical upper bound of $o(1)$ f(x) is o(g(x)) means that growth of f(x) is nothing compared to g(x). (Correct: it is upper bound) So maximum of $o(1)$ is $1$ so $x<2n\log n$. OK? Apr 3 comment Numerical upper bound of $o(1)$ No confusion. It is smallOh. I want to replace that smallO in upper bound (although smallO is usually for lower bound), with a number Mar 6 comment Proof of Generalized Primorial Primes Thank you, brilliant explanation ... Mar 3 comment Proof of Prime Maker Conjecture @Hans Engler, I've updated the algorithm with correct explaination Mar 2 comment Proof of Prime Maker Conjecture $d_0$ is a prime factor of $n$ or $m+1$, so $d_0 \mid m+1$, and so then we have $d_0 \not\mid d_0\times m + 1$. Got it? Mar 2 comment Proof of Prime Maker Conjecture To multiply $m$ by $d_0$ and put the result $+1$ into $n$. It is primorial of 100th prime. Dec 22 comment Modular arithmetic with different moduli thanks for your answer, but do you think the nonexistence of any property for the modulus addition or subtraction is due to the nature of modular arithmetic or due to that we didn't find any relation yet? Dec 14 comment Fundamental Period of sequence modulo N I assume that $N$ or $p$ is prime and I know full factorization of $N-1$. And I know all divisors of $N-1$. How do I know which divisor is $T$ (fundamental period)?. The real problem is this. Dec 14 comment Fundamental Period of sequence modulo N As I know, if there is any $T$ it should be among divisors of $N-1$. That is, in case of existence of such a $T$, it should be made from the prime factors of $N-1$ so $T$ is one of divisors of $N-1$. Dec 13 comment Fundamental Period of sequence modulo N thanks for answer. As I told in the question I want to obtain $T$, without calculating the modular exponentiation for all $T$ up to $N$. With calculation it is obvious that $2^{27} \equiv 2^1 \pmod{2731}$. So $T = 27-1 = 26$ Dec 11 comment Fundamental Period of sequence modulo N I know that it becomes a PRP only, but it is the first step in any deterministic test. Dec 11 comment Fundamental Period of sequence modulo N @AndréNicolas, your'true about composites.I'm looking to reduce the exponent for primility test. If I know $N$ is prime, then $N-1$ is an obvious member of the sequence Dec 10 comment Estimation on Primorial Influence @sunflower, you're true, I forgot to add $n\# + 1$ and $n\# - 1$ special cases. Question updated. Dec 6 comment Approaching Euler totient for arbitrary n Look at here math.stackexchange.com/questions/249982/… Dec 6 comment Approaching Euler totient for arbitrary n @GerryMyerson, every mathematics mystery has been solved by a conjecture and then proving, extending and correcting that.. The visual appearance of tree seems interesting so I asked to extend the idea Dec 5 comment Approaching Euler totient for arbitrary n Useful for small numbers but not for thousand digits numbers Dec 3 comment Fastest Primality test using $N-1$ Factorization? @Arthur, but the computation time doubled as I splited the exponentiation to factors !!! Dec 3 comment Fastest Primality test using $N-1$ Factorization? @TonyK can you please explain more. The modular exponentiation can't be parallelized. How do you mean? I was already working on parallel modular exponentiation mathematica.stackexchange.com/questions/15062/parallel-powermod and your note seems very interesting Dec 3 comment Fastest Primality test using $N-1$ Factorization? @Arthur, once I calculated $a^A$, can I reduce it $mod N$ then raise to $B$ ?