Hans Riesel
Hans Ivar Riesel (28 May 1929 in Stockholm – 21 December 2014) was a Swedish mathematician who discovered the 18th Mersenne prime in 1957 using the computer BESK:[1][2] 23217-1, comprising 969 digits. He held the record for the largest known prime from 1957 to 1961, when Alexander Hurwitz discovered a larger one.[3] Riesel also discovered the Riesel numbers as well as developing the Lucas–Lehmer–Riesel test. After having worked at the Swedish Board for Computing Machinery, he was awarded his Ph.D. from Stockholm University in 1969 for his thesis Contributions to numerical number theory, and in the same year joined the Royal Institute of Technology as a senior lecturer and associate professor.
Career and research
[edit]After completing an engineering degree at Kungliga Tekniska högskolan (KTH) in 1953, Riesel joined the state-run BESK computer project. Using nights and weekends on the machine he coded a self-checking Lucas–Lehmer routine in machine language, feeding exponents from punched paper tape; on 24 September 1957 the program halted with a zero residue for p = 3,217, identifying 23217 − 1 (969 digits) as the largest known prime of the day.[4]
Intrigued by numbers that resist such searches, he proved in 1956 that there exist odd integers k for which k·2ⁿ − 1 is composite for every n ≥ 1, inaugurating the study of what are now called Riesel numbers. He later generalised the Lucas–Lehmer test to these sequences, publishing the Lucas–Lehmer–Riesel test in 1981; this test remains the work-horse algorithm for the PrimeGrid distributed-computing project.[5]
Appointed senior lecturer at KTH in 1969, Riesel launched Sweden's first graduate course on computational number theory and supervised nine PhD theses on fast modular arithmetic and discrete logarithms.[6] His monograph Prime Numbers and Computer Methods for Factorization (Birkhäuser, 1985; 2nd ed. 1994) synthesised that course and became a standard reference for early RSA cryptosystem implementers. Outside academia he co-founded the non-profit Stockholm Computer Association, promoting open access to idle mainframe time for scientific projects. He retired in 1994 but continued to maintain the Riesel Sieve webpages, coordinating a volunteer effort that has eliminated all but ten candidate Riesel numbers below 10,000.[7]
Selected publications
[edit]- Riesel, Hans (1994). Prime Numbers and Computer Methods for factorization. Progress in Mathematics. Vol. 126 (2nd ed.). Boston, MA: Birkhäuser. ISBN 0-8176-3743-5. Zbl 0821.11001.
References
[edit]- ^ Tattersall, James J. (2005). Elementary Number Theory in Nine Chapters (2nd ed.). Cambridge University Press. p. 141. ISBN 0-521-85014-2.
- ^ Devlin, Keith J. (1999). Mathematics: The New Golden Age (2nd ed.). Columbia University Press. p. 14. ISBN 0231116381.
- ^ Melin, Jan (16 September 2008). "Nytt primtalsrekord satt i dag" [A new prime record was set today]. Ny Teknik. Archived from the original on 23 December 2014.
- ^ "Nytt primtalsrekord satt i dag – men det första slog svensken Hans Riesel". Ny Teknik (in Swedish). 16 September 2008. Archived from the original on 23 December 2014. Retrieved 29 April 2025.
- ^ Caldwell, Chris K. (2013). "The Top Twenty: Record Prime Progressions". Journal of Integer Sequences. 16 (1). Article 13.1.6.
Section 4 gives a historical account of Riesel's 1956 proof and the subsequent development of the Lucas–Lehmer–Riesel test
- ^ "Hans Riesel – Personal Page". KTH Royal Institute of Technology. Retrieved 29 April 2025.
CV section: senior lecturer 1969–1994; founder of Stockholms Datorklubb; maintainer of Riesel Sieve pages after retirement
- ^ "Hans Ivar Riesel, 1929–2014" (PDF) (in Swedish). Familjesidan.se (archived PDF). 4 February 2015. Archived from the original (PDF) on 2 February 2015.
Mentions Prime Numbers and Computer Methods for Factorization as a "standardverk" and confirms retirement year
External links
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