Smarandache Factors and Reverse Factors Micha Fleuren November 1998
Abstract This document will describe the current status on the search for factors of Smaranda.che consecutive numbers and their reverse. A complete list up to index 200 will be given, with all known factors. Smarandache numbers are the concatenation of the natural numbers from one up to the given index, and reverse Smaranda.che numbers are the concatenation of the natural numbers from the given index dO\vIJ. to 1.
1
Introduction
As a followup to Ralf Stephan's article in this journal [St], I decided to extend his factorizations to index 200. The Smarandache consecutive sequence, as well as their reverse is described in [Sm]. In this article Sm11 denotes 1234567891011 for example, and Rsm11 denotes 111098765432l. Most of the factors that have been found by me and others, have been found by using the elliptic curve method (ECM) [Le], some have been found using the Multiple Polynomial Quadratic Sieve (MPQS) [Silo All factors and remaining cofactors have been proven prime or composite by means of Elliptic Curve Primality Proving (ECPP) [At], or the AdlemanPomerance-Rumely test [Ad], which has been simplified in 1984 by Cohen and Lenstra [Co].
2
Software used
The main factoring program used has been GMP-ECM by Paul Zimmermann [Zi, Le, Grl. The first small factors were filtered out quickly by ECMX, a program of the UBASIC package [KL Lel.
5