PRIMES is in P
نویسندگان
چکیده
منابع مشابه
PRIMES is in P
We present an unconditional deterministic polynomial-time algorithm that determines whether an input number is prime or composite.
متن کاملAaron Wootton STUDY OF “ PRIMES IS IN P ”
This paper is an in depth study of “Primes is in P .” It details the proofs presented in [1], and includes a proof of the time complexity. It also explains how the algorithm was implemented in various programming languages. We finish by laying out future plans for how to improve the algorithm and further work to be investigated.
متن کاملPrimes is in P for a large family of numbers
Sharpening Primes is in P for a large family of numbers. Abstract We present algorithms that are deterministic primality tests for a large family of integers, namely, integers n ≡ 1 (mod 4) for which an integer a is given such that the Jacobi symbol (a n) = −1, and integers n ≡ −1 (mod 4) for which an integer a is given such that (a n) = (1−a n) = −1. The algorithms we present run in 2 − min(k,...
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We discuss the problem of finding a p-adic L-function attached to an elliptic curve with complex multiplication over an imaginary quadratic field K, for the case of a prime where the curve has supersingular reduction. While the case of primes of ordinary reduction has been extensively studied and is essentially understood, yielding many deep and interesting results, basic questions remain unans...
متن کاملConstructing x 2 for primes p = ax
Let a and b be positive integers and let p be an odd prime such that p = ax2+by2 for some integers x and y. Let λ(a, b;n) be given by q ∏∞ k=1(1−q)(1−q) = ∑∞ n=1 λ(a, b;n)q n. In this paper, using Jacobi’s identity ∏∞ n=1(1−q) = ∑∞ k=0(−1)(2k+1)q k(k+1) 2 , we construct x2 in terms of λ(a, b;n). For example, if 2 ab and p ab(ab+1), then (−1)a+b 2 x+ b+1 2 (4ax2−2p) = λ(a, b; ((ab + 1)p − a − b)...
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2004
ISSN: 0003-486X
DOI: 10.4007/annals.2004.160.781