Hans Ivar Riesel (28 May 1929 in

Stockholm Stockholm (; ) is the Capital city, capital and List of urban areas in Sweden by population, most populous city of Sweden, as well as the List of urban areas in the Nordic countries, largest urban area in the Nordic countries. Approximately ...

– 21 December 2014) was a

Swedish Swedish or ' may refer to: Anything from or related to Sweden, a country in Northern Europe. Or, specifically: * Swedish language, a North Germanic language spoken primarily in Sweden and Finland ** Swedish alphabet, the official alphabet used by ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

who discovered the 18th

Mersenne prime In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 1 ...

in 1957 using the computer

BESK BESK (''Binär Elektronisk SekvensKalkylator'', Swedish language, Swedish for "Binary Electronic Sequence Calculator") was Sweden's first electronic computer, using vacuum tubes instead of relays. It was developed by ''Matematikmaskinnämnden ...

: 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. Riesel also discovered the

Riesel number In mathematics, a Riesel number is an odd natural number ''k'' for which k\times2^n-1 is composite for all natural numbers ''n'' . In other words, when ''k'' is a Riesel number, all members of the following set are composite: :\left\. If the for ...

s as well as developing the

Lucas–Lehmer–Riesel test In mathematics, the Lucas–Lehmer–Riesel test is a primality test for numbers of the form with odd . The test was developed by Hans Riesel and it is based on the Lucas–Lehmer primality test. It is the fastest deterministic algorithm known ...

. After having worked at the

Swedish Board for Computing Machinery The Swedish Board for Computing Machinery (, MMN) was a Swedish government agency which built Sweden's first computers: BARK and BESK. A governmental study into the need for computing machinery in Sweden had been conducted in 1947 by initiative o ...

, he was awarded his

Ph.D. A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...

from

Stockholm University Stockholm University (SU) () is a public university, public research university in Stockholm, Sweden, founded as a college in 1878, with university status since 1960. With over 33,000 students at four different faculties: law, humanities, social ...

in 1969 for his thesis ''Contributions to numerical number theory'', and in the same year joined the

Royal Institute of Technology KTH Royal Institute of Technology (), abbreviated KTH, is a public research university in Stockholm, Sweden. KTH conducts research and education in engineering and technology and is Sweden's largest technical university. Since 2018, KTH consist ...

as a senior lecturer and associate professor.

Career and research

After completing an

engineering Engineering is the practice of using natural science, mathematics, and the engineering design process to Problem solving#Engineering, solve problems within technology, increase efficiency and productivity, and improve Systems engineering, s ...

degree at

Kungliga Tekniska högskolan KTH Royal Institute of Technology (), abbreviated KTH, is a public research university in Stockholm, Sweden. KTH conducts research and education in engineering and technology and is Sweden's largest technical university. Since 2018, KTH consist ...

(KTH) in 1953, Riesel joined the state-run

computer project. Using nights and weekends on the machine he coded a self-checking Lucas–Lehmer routine in

machine language In computer programming, machine code is computer code consisting of machine language instructions, which are used to control a computer's central processing unit (CPU). For conventional binary computers, machine code is the binaryOn nonb ...

, feeding exponents from punched

paper tape Five- and eight-hole wide punched paper tape Paper tape reader on the Harwell computer with a small piece of five-hole tape connected in a circle – creating a physical program loop Punched tape or perforated paper tape is a form of data st ...

; 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. Intrigued by numbers that resist such searches, he proved in 1956 that there exist odd

integer An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...

s k for which k·2ⁿ − 1 is

composite Composite or compositing may refer to: Materials * Composite material, a material that is made from several different substances ** Metal matrix composite, composed of metal and other parts ** Cermet, a composite of ceramic and metallic material ...

for every n ≥ 1, inaugurating the study of what are now called

s. He later generalised the Lucas–Lehmer test to these sequences, publishing the

in 1981; this test remains the work-horse

algorithm In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...

for the

PrimeGrid PrimeGrid is a volunteer computing project that searches for very large (up to world-record size) prime numbers whilst also aiming to solve long-standing mathematical conjectures. It uses the Berkeley Open Infrastructure for Network Computing ( ...

distributed-computing project. Appointed senior lecturer at KTH in 1969, Riesel launched Sweden's first graduate course on

computational number theory In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithm ...

and supervised nine PhD theses on fast

modular arithmetic In mathematics, modular arithmetic is a system of arithmetic operations for integers, other than the usual ones from elementary arithmetic, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to mo ...

and

discrete logarithm In mathematics, for given real numbers a and b, the logarithm \log_b(a) is a number x such that b^x=a. Analogously, in any group G, powers b^k can be defined for all integers k, and the discrete logarithm \log_b(a) is an integer k such that b^k=a ...

s. His

monograph A monograph is generally a long-form work on one (usually scholarly) subject, or one aspect of a subject, typically created by a single author or artist (or, sometimes, by two or more authors). Traditionally it is in written form and published a ...

''Prime Numbers and Computer Methods for Factorization'' (Birkhäuser, 1985; 2nd ed. 1994) synthesised that course and became a standard reference for early

RSA cryptosystem The RSA (Rivest–Shamir–Adleman) cryptosystem is a public-key cryptosystem, one of the oldest widely used for secure data transmission. The initialism "RSA" comes from the surnames of Ron Rivest, Adi Shamir and Leonard Adleman, who publicly ...

implementers. Outside academia he co-founded the non-profit Stockholm Computer Association, promoting open access to idle

mainframe A mainframe computer, informally called a mainframe or big iron, is a computer used primarily by large organizations for critical applications like bulk data processing for tasks such as censuses, industry and consumer statistics, enterpris ...

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.

Selected publications

References

External links

Riesel's web pageObituary
{{DEFAULTSORT:Riesel, Hans 1929 births 2014 deaths Number theorists Academic staff of the KTH Royal Institute of Technology Swedish mathematicians People from Stockholm