Karl Dilcher
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Research Interests
Karl Dilcher has a total of 6 co-authors. Here are the top co-authors by number of shared publications:
- Richard Crandall
Center for Advanced Computation, Reed College, Portland, Oregon 97202
2 shared publications - C. Van Halewyn
Department of Computer Science and Engineering, Oregon Graduate Institute
1 shared publication - Carl Pomerance
Department of Mathematics, University of Georgia, Athens, Georgia 30602
1 shared publication - Ladislav Skula
Department of Mathematics and Statistics Faculty of Science Masaryk University Kotlářská 2 611 37 Brno Czech Republic
1 shared publication - Richard P. Brent
Australian National University
1 shared publication - Takashi Agoh
Science University of Tokyo
1 shared publication
Latest Publications
- Open Access
- 1 March 2000
- Published by American Mathematical Society (AMS) in Mathematics of Computation
- Vol. 69 (231) , 1297-1304
Three new factors of Fermat numbers
We report the discovery of a new factor for each of the Fermat numbers F 13 , F 15 , F 16 F_{13}, F_{15}, F_{16} . These new factors have 27, 33 and 27 decimal digits respectively. Each factor was found by the elliptic curve method. After division by the new factors and previously known factors, the remaining cofactors are seen to be composite numbers with 2391 2391 , 9808 9808 and 19694 19694 decimal digits respectively.
- 1 March 2000
- Published by American Mathematical Society (AMS) in Mathematics of Computation
- Vol. 69 (231) , 1297-1304
Open AccessThree new factors of Fermat numbers
We report the discovery of a new factor for each of the Fermat numbers F 13 , F 15 , F 16 F_{13}, F_{15}, F_{16} . These new factors have 27, 33 and 27 decimal digits respectively. Each factor was found by the elliptic curve method. After division by the new factors and previously known factors, the remaining cofactors are seen to be composite numbers with 2391 2391 , 9808 9808 and 19694 19694 decimal digits respectively.
- 1 September 1997
- Published by Elsevier in Journal of Number Theory
- Vol. 66 (1) , 29-50
Fermat Quotients for Composite Moduli
- 1 September 1997
- Published by Elsevier in Journal of Number Theory
- Vol. 66 (1) , 29-50
Fermat Quotients for Composite Moduli
- Open Access
- 1 January 1997
- Published by American Mathematical Society (AMS) in Mathematics of Computation
- Vol. 66 (217) , 433-450
A search for Wieferich and Wilson primes
An odd prime is called a Wieferich prime if
- 1 January 1997
- Published by American Mathematical Society (AMS) in Mathematics of Computation
- Vol. 66 (217) , 433-450
Open AccessA search for Wieferich and Wilson primes
An odd prime is called a Wieferich prime if
- 1 July 1992
- Published by JSTOR in Mathematics of Computation
- Vol. 59 (199) , 259-282
Generalized Euler Constants for Arithmetical Progressions
The work of Lehmer and Briggs on Euler constants in arithmetical progressions is extended to the generalized Euler constants that arise in the Laurent expansion of $\zeta (s)$ about $s = 1$. The results are applied to the summation of several classes of slowly converging series. A table of the constants is provided.- 1 July 1992
- Published by JSTOR in Mathematics of Computation
- Vol. 59 (199) , 259-282
Generalized Euler Constants for Arithmetical Progressions
The work of Lehmer and Briggs on Euler constants in arithmetical progressions is extended to the generalized Euler constants that arise in the Laurent expansion of $\zeta (s)$ about $s = 1$. The results are applied to the summation of several classes of slowly converging series. A table of the constants is provided.