Solovay-Strassen test

Let's check the numbers using Solovay-Strassen primality test .

Let's start with 201. The Solovay- Strassen primality test says that if $(a/n)≢ a^\frac{n-1}{2}\ (mod n)$ , (a is an integer coprime to n), then n is a composite number. Now let's look how it works with 201: We have to compute 201^201 mod 403 because (403-1)/2 = 201.

$(201)^201=((201)^3))^67 ≡(151)^67=151∙((151)^2 )^33 ≡151∙(233)^33=151∙((233)^3 )^11≡ 151∙ 376^11= 151∙376∙((376)^2)^5≡356∙(326)^5=356∙(326)^3∙(326)^2≡356∙66 ∙287=6743352 ≡356 (mod 403)$

We got the remainder 356 and it can't be equal to Jacobi symbol. So the answer is 201 .