Doubly-Focused Enumeration of Pseudosquares and Pseudocubes (DRAFT)

نویسندگان

  • Kjell Wooding
  • H. C. Williams
چکیده

This paper offers numerical evidence for a conjecture that primality proving may be done in (logN) operations by examining the growth rate of quantities known as pseudosquares and pseudocubes. In the process, a novel method of solving simultaneous congruences— doubly-focused enumeration— is examined. This technique, first described by D. J. Bernstein, allowed us to obtain record-setting sieve computations in software on general purpose computers.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A formula for the doubly refined enumeration of alternating sign matrices

Zeilberger [12] proved the Refined Alternating Sign Matrix Theorem, which gives a product formula, first conjectured by Mills, Robbins and Rumsey [9], for the number of alternating sign matrices with given top row. Stroganov [10] proved an explicit formula for the number of alternating sign matrices with given top and bottom rows. Fischer and Romik [7] considered a different kind of “doubly-ref...

متن کامل

A formula for a doubly refined enumeration of alternating sign matrices

Zeilberger [12] proved the Refined Alternating Sign Matrix Theorem, which gives a product formula, first conjectured by Mills, Robbins and Rumsey [9], for the number of alternating sign matrices with given top row. Stroganov [10] proved an explicit formula for the number of alternating sign matrices with given top and bottom rows. Fischer and Romik [7] considered a different kind of “doubly-ref...

متن کامل

Some results on pseudosquares

If p is an odd prime, the pseudosquare Lp is defined to be the least positive nonsquare integer such that Lp ≡ 1 (mod 8) and the Legendre symbol (Lp/q) = 1 for all odd primes q ≤ p. In this paper we first discuss the connection between pseudosquares and primality testing. We then describe a new numerical sieving device which was used to extend the table of known pseudosquares up to L271. We als...

متن کامل

The Enumeration of Doubly Alternating Baxter Permutations

In this paper, we give an alternative proof that the number of doubly alternating Baxter permutations is Catalan.

متن کامل

Highly depressed temperature-induced metal-insulator transition in synthetic monodisperse 10-nm V2O3 pseudocubes enclosed by {012} facets.

Monodisperse 10-nm V(2)O(3) pseudocubes enclosed by {012} facets were successfully synthesized for the first time via a novel and facile solvothermal method, offering the first opportunity to elucidate the effect of finite-size and facet on the temperature-induced reversible metal-insulator transition (MIT) behavior of V(2)O(3). Very excitingly, the transition temperature of these V(2)O(3) pseu...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2006