Results

**21 - 28**of**28**### PALINDROMIC PRIME PYRAMIDS

"... Have you ever seen the great stone pyramids of ancient Egypt or Central America? For over 5000 years, mankind has been building, visiting, and even sleeping in pyramids. When Memphis, Tennessee, decided to build a new arena in 1991, they chose the shape of a pyramid— this time constructed of steel a ..."

Abstract
- Add to MetaCart

(Show Context)
Have you ever seen the great stone pyramids of ancient Egypt or Central America? For over 5000 years, mankind has been building, visiting, and even sleeping in pyramids. When Memphis, Tennessee, decided to build a new arena in 1991, they chose the shape of a pyramid— this time constructed of steel and glass rather than rock and rubble. In this paper we also build pyramids, ours built of the unbreakable stones of mathematics: the primes. But not just any primes, we have chosen the symmetry of nested palindromes as mortar. For example, beginning with the prime 2, we can build two pyramids of height five. (Unlike the ancients, we build our pyramids from the top down.)

### On the primality of F 4723 and F 5387

, 1999

"... Introduction We follow the notations of both [2] and [3]. Let F n (resp. L n ) be the n-th Fibonacci number (resp. Lucas number). The aim of this informal note is to describe a short proof of primality for both F 4723 and F 5387 . See the paper [5] for more on this topic. 2 F 4723 From [3, (4.1)], ..."

Abstract
- Add to MetaCart

Introduction We follow the notations of both [2] and [3]. Let F n (resp. L n ) be the n-th Fibonacci number (resp. Lucas number). The aim of this informal note is to describe a short proof of primality for both F 4723 and F 5387 . See the paper [5] for more on this topic. 2 F 4723 From [3, (4.1)], one has F 4k+3 \Gamma 1 = F k+1 L k+1 L 2k+1 : (1) Here k = 1180, k + 1 = 1181 and 2k + 1 = 2361 = 3 \Theta 787. From [3] and with the help of factors found by Montgomery and Silverman [7, 8, 9], we get F 1181 = 5453857 \Theta C 240 ; L 1181 = 59051 \Theta<F27.43

### A New World Record for the Special Number Field Sieve Factoring Method

, 1997

"... 25> f(a=b) and of a=b\Gammam are both smooth, meaning that only small prime factors divide these numerators. These are more likely to be smooth when 1 We assume the reader to be familiar with this factoring method, although no expert knowledge is required to understand the spirit of this announ ..."

Abstract
- Add to MetaCart

25> f(a=b) and of a=b\Gammam are both smooth, meaning that only small prime factors divide these numerators. These are more likely to be smooth when 1 We assume the reader to be familiar with this factoring method, although no expert knowledge is required to understand the spirit of this announcement. 2 NFSNET is a collaborative effort to factor numbers by the Number Field Sieve. It relies on volunteers from around the world who contribute the "spare time" of a large number of workstations to perform the sieving. In addition to completing work on other numbers, their 75 workstations sieved (3 349 \Gamma 1)=2 during the months of December 1996 and January 1997. The organizers and principal researchers of NFSNET are: Marije ElkenbrachtHuizing, Peter Montgomery, Bob Silverman, Richard Wackerbarth, and Sam Wagstaff, Jr. 1. the polynomial values themselves are

### Pseudoprimes: A Survey Of Recent Results

, 1992

"... this paper, we aim at presenting the most recent results achieved in the theory of pseudoprime numbers. First of all, we make a list of all pseudoprime varieties existing so far. This includes Lucas-pseudoprimes and the generalization to sequences generated by integer polynomials modulo N , elliptic ..."

Abstract
- Add to MetaCart

this paper, we aim at presenting the most recent results achieved in the theory of pseudoprime numbers. First of all, we make a list of all pseudoprime varieties existing so far. This includes Lucas-pseudoprimes and the generalization to sequences generated by integer polynomials modulo N , elliptic pseudoprimes. We discuss the making of tables and the consequences on the design of very fast primality algorithms for small numbers. Then, we describe the recent work of Alford, Granville and Pomerance, in which they prove that there

### Accessed: 08/04/2009 10:26

"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."

Abstract
- Add to MetaCart

(Show Context)
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at

### Article 01.2.3 Prime Pythagorean triangles

"... A prime Pythagorean triangle has three integer sides of which the hypotenuse and one leg are primes. In this article we investigate their properties and distribution. We are also interested in finding chains of such triangles, where the hypotenuse of one triangle is the leg of the next in the sequen ..."

Abstract
- Add to MetaCart

(Show Context)
A prime Pythagorean triangle has three integer sides of which the hypotenuse and one leg are primes. In this article we investigate their properties and distribution. We are also interested in finding chains of such triangles, where the hypotenuse of one triangle is the leg of the next in the sequence. We exhibit a chain of seven prime Pythagorean triangles and we include a brief discussion of primality proofs for the larger elements (up to 2310 digits) of the associated set of eight primes.

### Prime Pythagorean triangles

, 2001

"... A prime Pythagorean triangle has three integer sides of which the hypotenuse and one leg are primes. In this article we investigate their properties and distribution. We are also interested in finding chains of such triangles, where the hypotenuse of one triangle is the leg of the next in the sequen ..."

Abstract
- Add to MetaCart

(Show Context)
A prime Pythagorean triangle has three integer sides of which the hypotenuse and one leg are primes. In this article we investigate their properties and distribution. We are also interested in finding chains of such triangles, where the hypotenuse of one triangle is the leg of the next in the sequence. We exhibit a chain of seven prime Pythagorean triangles and we include a brief discussion of primality proofs for the larger elements (up to 2310 digits) of the associated set of eight primes. 1991 Mathematics Subject Classification: Primary 11A41 Keywords: Pythagorean triangles, prime numbers, primality proving 1.