THE DISTRIBUTION OF PRIME NUMBERS Andrew Granville and K
... will prove theorems on π(x) and π(x; q, a), the number of primes up to x that are ≡ a (mod q), focussing on uniformity in x, including the Bombieri-Vinogradov theorem, and a new simpler proof of Linnik’s theorem as well as Vinogradov’s three primes theorem. We will prove an improved Polya-Vinogradov ...
... will prove theorems on π(x) and π(x; q, a), the number of primes up to x that are ≡ a (mod q), focussing on uniformity in x, including the Bombieri-Vinogradov theorem, and a new simpler proof of Linnik’s theorem as well as Vinogradov’s three primes theorem. We will prove an improved Polya-Vinogradov ...
On some polynomial-time primality algorithms
... Table 1.1: Cardinality of the psp(2) set below x This table (based on [11] and [8]), let us make the hypothesis that the number of pseudoprimes in base 2 are significantly smaller than π(x). In fact in Crandall-Pomerance [3] we have the following theorem. Theorem 1.2. For each fixed integer a ≥ 2, t ...
... Table 1.1: Cardinality of the psp(2) set below x This table (based on [11] and [8]), let us make the hypothesis that the number of pseudoprimes in base 2 are significantly smaller than π(x). In fact in Crandall-Pomerance [3] we have the following theorem. Theorem 1.2. For each fixed integer a ≥ 2, t ...
A Guide to Your Modular Math Course Contents Joseph Lee Fall 2014
... Mod 22 - Sec 3.5 A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Mod 22 - Sec 4.1 A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Mod 22 - Sec 4.2 A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
... Mod 22 - Sec 3.5 A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Mod 22 - Sec 4.1 A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Mod 22 - Sec 4.2 A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
Generalised Frobenius numbers: geometry of upper bounds
... finding the index of primitivity γ(B) of a nonnegative matrix B = (bi,j ) (i.e. bi,j ≥ 0), 1 ≤ i, j ≤ k of order (ak + ak−1 − 1) via graph theory F(a1 , . . . , ak ) = γ(B) − 2ak + 1 , where γ(B) is the smallest integer such that B γ(B) > 0. We note that other methods have been derived, but they wil ...
... finding the index of primitivity γ(B) of a nonnegative matrix B = (bi,j ) (i.e. bi,j ≥ 0), 1 ≤ i, j ≤ k of order (ak + ak−1 − 1) via graph theory F(a1 , . . . , ak ) = γ(B) − 2ak + 1 , where γ(B) is the smallest integer such that B γ(B) > 0. We note that other methods have been derived, but they wil ...
