Wilfrid Keller

Current address:
Badestrasse 5
20148 Hamburg
Germany

e-mail:  wilfrid.keller@gmx.net


Curriculum Vitae

1937: Born in Wetzlar, Germany. Moved to Buenos Aires, Argentina.
1943−1954: Attended primary and secondary school in Buenos Aires.
1955−1962: Studied mathematics at the Universidad Nacional de Buenos Aires.
1962: Obtained degree of Licenciado en Ciencias Matemáticas.
1963: Returned to Germany, settled in Hamburg.
1963−1969: Fellowship of Deutscher Akademischer Austauschdienst (DAAD).
1963−1970: Studied numerical mathematics and economics at Universität Hamburg.
1970: Obtained degree of Doctor rerum naturalium.
1970−1998: Member of staff of Regionales Rechenzentrum der Universität Hamburg.
1999: Retired from public service.

Member of Mathematische Gesellschaft in Hamburg, Deutsche Mathematiker-Vereinigung (DMV), American Mathematical Society (AMS).

Publications

Thesis

Asymptotische Aussagen und Fehlerabschätzungen für eine Klasse linearer Integro-Differential-Differenzengleichungen als Folge von Monotonieeigenschaften gewöhnlicher Anfangswertaufgaben (Supervisor: Lothar Collatz). Universität Hamburg, 1970, 75 pages.

Abstracts

Preliminary reports published in Abstracts of the American Mathematical Society.

  1. Large twin prime pairs related to Mersenne numbers, 4 (1983), 490.
  2. New factors of Fermat numbers, 5 (1984), 391−392.
  3. The 17th prime of the form 5 · 2n + 1, 6 (1985), 121.
  4. The Carmichael numbers up to 1013, 9 (1988), 328−329.
  5. The least prime of the form k · 2n + 1 for certain values of k, 9 (1988), 417−418.
  6. New prime solutions p of a p-1 = 1 (mod p2), 9 (1988), 503.
  7. Richard G. E. Pinch and ____, The Carmichael numbers up to 1015, 13 (1992), 505.
  8. ____ and François Morain, The complete factorization of some large Mersenne composites, 13 (1992), 506.
  9. Harvey Dubner and ____, New Fibonacci and Lucas primes, 16 (1995), 267.
  10. Prime solutions p of a p-1 = 1 (mod p2) for prime bases a, 19 (1998), 394.
  11. ____ and Jörg Richstein, Prime solutions p of a p-1 = 1 (mod p2) for prime bases a, II, 20 (1999), 228.
  12. Harvey Dubner and ____, Some large prime primitive parts of Fibonacci and Lucas numbers, 21 (2000), 248.
  13. Günter Löh and ____, Generalized Cullen primes, 25 (2004), 440−441.

Papers

  1. Factors of Fermat numbers and large primes of the form k · 2n + 1, Mathematics of Computation 41 (1983), 661−673. MR 85b:11117.
  2. ____ and Günter Löh, The criteria of Kummer and Mirimanoff extended to include 22 consecutive irregular pairs, Tokyo Journal of Mathematics 6 (1983), 397−402; Supplement, ibid, 487. MR 85h:11014.
  3. Woher kommen die größten derzeit bekannten Primzahlen?, Mitteilungen der Mathematischen Gesellschaft in Hamburg XII (1991), 211−229. MR 92j:11006.
  4. Harvey Dubner and ____, Factors of generalized Fermat numbers, Mathematics of Computation 64 (1995), 397−405. MR 95c:11010.
  5. New Cullen primes, Mathematics of Computation 64 (1995), 1733−1741; Supplement (with Wolfgang Niebuhr), ibid, S39−S46. MR 95m:11015.
  6. ____ et Leopoldo Kulesz, Courbes algébriques de genre 2 et 3 possédant de nombreux points rationnels, Comptes Rendus de l'Académie des Sciences (I) 321 (1995), 1469−1472. MR 96i:11072.
  7. Harvey Dubner and ____, New Fibonacci and Lucas primes, Mathematics of Computation 68 (1999), 417−427; Supplement, ibid, S1−S12. MR 99c:11008.
  8. ____ and Jörg Richstein, Solutions of the congruence a p-1 = 1 (mod pr), Mathematics of Computation 74 (2005), 927−936. MR 2005i:11004.
  9. Chris K. Caldwell, Angela Reddick, Yeng Xiong, and ____, The history of the primality of One: A selection of sources, Journal of Integer Sequences 15 (2012), Article 12.9.8, 40 pages. MR 3005523.

Preprints

  1. Factors of Fermat numbers and large primes of the form k · 2n + 1. II, 40 pages + 20 tables, 27 September 1992.
  2. Factors of generalized Fermat and Mersenne numbers, 13 pages + 5 tables, 7 September 1995.

Tables

  1. Factors of Mersenne numbers Mp for p < 100000, Hamburg, 1977; cf. abstract #8.
  2. Primes of the form k · 2n + 1, k odd, for k < 1200 and n ≤ 1000, Hamburg, 1980; cf. paper #4 and preprint #1. 
  3. Factors of Cullen numbers Cn and Woodall numbers Wn for 300 < n ≤ 1000; cf. paper #5.
    For an up-to-date account, see the tables maintained by Paul Leyland, http://www.leyland.vispa.com/numth/factorization/cullen_woodall/cw.html .
  4. Factors of Fibonacci numbers Fn (n odd) and Lucas numbers Ln for 1000 < n < 9750; cf. paper #7.
    For an extended and up-to-date account, see the site maintained by Blair Kelly, http://mersennus.net/fibonacci/index.html.

Web pages

  1. Ray Ballinger and ____, List of primes k · 2n + 1 for k < 300>
    http://www.prothsearch.net/riesel.html, since April 1998; extended to k < 600 in September extended to>k < 1200 in June> 
  2. Prime factors k · 2n + 1 of Fermat numbers Fm and complete factoring status,
    http://www.prothsearch.net/fermat.html, since April 1998. 
  3. ____ and Jörg Richstein, Fermat quotients qp(a) that are divisible by p,
    http://www.rrz.uni-hamburg.de/RRZ/W.Keller/FermatQuotient.html, since September 1998, reworked February 2009. 
  4. The Sierpiński problem: Definition and status,
    http://www.prothsearch.net/sierp.html, since November 1998, unchanged since November 2002, reworked February 2010. 
  5. The Riesel problem: Definition and status,
    http://www.prothsearch.net/rieselprob.html, since November 1998, unchanged since July 2008, reworked December 2010. 
  6. List of primes k · 2n − 1 for k < 300>
    http://www.prothsearch.net/riesel2.html, since December 1998. 
  7. Prime factors k · 2n + 1 of generalized Fermat numbers, since December 2001:  
  8. Factors of generalized Fermat numbers found after Björn & Riesel,
    http://www.prothsearch.net/GFNfacs.html, since December 2003. 
  9. Factorization of generalized Fermat numbers for small indices m,
    http://www.prothsearch.net/GFsmall.html, since January 2004. 
  10. Prime factors k · 2n + 1 of generalized Fermat numbers, since December 2008:  

Participation in a book project

Updates to "Paulo Ribenboim, Die Welt der Primzahlen: Geheimnisse und Rekorde", translated from the English by Jörg Richstein. Springer-Verlag, Berlin and Heidelberg, September 2006, xxiii + 356 pages; second, completely revised edition, March 2011, xxv + 366 pages.

This page maintained by Wilfrid Keller. Last modified December 18, 2013.